Did Germany offer the Soviet Union an opportunity to join the Axis?

In case you are interested in primary sources, here is one, from "Alexander N. Yakovlev's Archives", here.

Документ № 172. "Беседа председателя Совнаркома, наркома иностранных дел СССР В.М. Молотова с рейхсканцлером Германии А. Гитлером в Берлине." 12.11.1940.

... Гитлер отвечает, что тройственный пакт предусматривает руководящую роль в Европе для двух государств в областях их естественных интересов. Советскому Союзу предоставляется указать те области, в которых он заинтересован. То же в отношении великого восточно-азиатского пространства — Советский Союз должен сам сказать, что его интересует. Он, Гитлер, предлагает Советскому Союзу участвовать как четвертому партнеру в этом пакте. Гитлер считал, что с Советским Союзом можно будет договориться, что раньше состоялись переговоры с Италией и Францией, а теперь, когда с ними вопрос выяснен, он счел своевременным пригласить Советский Союз с тем, чтобы СССР высказался о своих интересах. Те вопросы, которые Советский Союз имеет по отношению к Румынии, Болгарии и Турции, нельзя решить здесь за 10 минут, и это должно быть предметом дипломатических переговоров. Мы все являемся континентальными государствами, хотя каждая страна имеет свои интересы. Америка же и Англия не являются континентальными государствами, они лишь стремятся к натравливанию европейских государств друг на друга, и мы хотим их исключить из Европы. Должен быть создан определенный мировой порядок, который будет иметь свои сферы интересов....

In case you do not read Russian, this is the Soviet record of Molotov's conversation with Hitler in Berlin, on November 12, 1940. My translation of the key sentences is:

Hitler replies that the tripartite pact provides for a leading role in Europe for the two states [Germany and Italy] in the areas of their natural interests. The Soviet Union is allowed to indicate those areas in which it is interested. The same with regard to the great East Asian space - the Soviet Union itself must say what its interests are. He, Hitler, invites the Soviet Union to participate as the fourth partner in this pact.

To the best of my understanding of your question (at least, the question which appears in the title), this quote provides a conclusive answer.

Remark. Regarding your complaint (in comments) that the above is taken out of context and is not an indication of high-level talks: I have no idea what this might possibly mean. Talks between Hitler and Molotov are as high-level as they could possibly be. (The only higher level would be direct talks between Hitler and Stalin, but as far as I know, neither one, when in power, ever visited a foreign country unoccupied by their army, so such talks could not have possibly happened.) If you mean that Hitler was simply shooting the breeze and was not making a serious proposal - sorry, I cannot take this conjecture seriously. During the meeting he explains to Molotov (Soviet Prime Minister as well as the Foreign Minister at the time and a member of the Politburo) his "new world order" based on a division of Eurasia into spheres of influence (excluding US and Great Britain as "non-continental powers") and invites USSR to participate. He also mentions areas of contention (e.g. Turkey, Romania, Bulgaria) that would have to be sorted out before the agreement on spheres of influence can be reached. (Click on the link that I gave above and use your favorite translation program from Russian to whatever language you prefer to read the details.)

And, indeed, the sides never managed to come to an agreement and USSR never joined the Axis, as we all know. But that was not because of lack of an invitation or lack of trying. Stalin simply wanted more than Hitler was willing to offer, differences were too high to overcome. If your question is really about details of the Soviet demands, you should edit your question to make this clear.

You are confusing the dates and two separate German-Soviet negotiations. The German-Soviet "Non-aggression pact" (Also called the Molotov-Ribbentrop pact) was signed in Moscow on 23 August 1939. This pact had a secret protocol, dividing the "spheres of influence". The result was a partition of Poland, and Soviet conquests of the Baltic countries and attempts at the conquest of Finland (Winter war).

The talks which included the German proposal for the Soviets to join the Axis were in Berlin in November 1940. Molotov visited Berlin and had talks with Hitler. The talks were a failure, because they could not agree on several points: the Soviets wanted a green light for a second invasion of Finland, wanted to have Bulgaria in the Soviet "sphere of interests", Soviet control of the straights etc. These were the main Soviet conditions for joining the Three-Partite Pact. The Germans instead tried to direct Soviet conquests to Asia, and insisted that they leave the rest of Europe alone.

After Molotov left, an official offer to join the Axis was still sent to Moscow, they replied with their conditions, and on this there was no German reply.

In the interval between these two negotiations, Germans invaded Poland, France, Belgium, Netherlands, Denmark and Norway, and started to plan an invasion of Soviet union since summer 1940. In the same period, Soviets conquered a larger part of Poland, 3 Baltic countries, a part of Finland and a part of Rumania, and planned to conquer the whole Finland, Bulgaria and wrestle the straits from the Turks.

There are many books which describe the story of Soviet German relations of that time in detail, but you may start with Wikipedia article. Of course, Stalin's book is a piece of propaganda (directed mainly at the Soviet population which had no other sources of information). He never mentions the 1940 unsuccessful negotiations, or German proposals to join the Axis.

Remark. The Tripartite pact (Germany-Italy-Japan=Axis) was signed on 27 September 1940, that is AFTER the Molotov-Ribbentrop pact of 1939. And the offer for Soviet union to join was made soon after that.

Remark. Soviet officials and historians always denied the existence of the secret protocol of 1939, until the demise of Soviet Union. After that the originals with Stalin signature and with the map of partition of Eastern Europe were published by the Russians.

Primary sources (translated into English):

Sontag, Raymond James, and James Stuart Beddie, eds. Nazi-Soviet relations, 1939-1941: Documents from the archives of the German foreign office (US Department of State, 1948) online.