Was there contact between the Inca, Maya and Aztecs?

There was plenty of contact between inca and maya. Aztec expeditions reached Maya borderlands. See maps! They were not that far away. Contacts are broadly attested in archeology (lots of knives and arrow points). Contacts are also attested in early 1500 oral tradition. Plus, “logical” trade routes easily connect the “aztec” Mexican highlands (good place to live) with the mayan Gulf and Yucatan coast and jungle plains (good place to live), passing through the mexican lowlands (really bad place to live). The Spanish used these networks extensively. This is fairly known and no historian doubts about that.

The contact was usually not direct, but it reached really far away. See the Etowah plates, in the Mississipi river, and tell me they are not of Mayan influence. Thus far the trade networks reached!

Incas contact is different. Incas did not have contact with Mayas or Aztecs, but Incas had coastal sea routes up to Panama. On the arrival, the Spanish watched indian canoes bringing goods from north to south using this route, and in the upper northern part, incas did exchange goods with indians further north. Those merchans told the spanish about the incan empire, already in the Panama ATLANTIC coast. In fact, if I remember correctly, I think I read some years ago that some gold found in incan jewelry did come from the Carribean area (lesser antilles and Veneçuela). That is something archeologists can chemically compare easily today, because each gold mine produces gold with slightly different purity.

Although not an answer regarding contact, an argument against regular trade between Inca and the other two could be made on the basis of rarity of golden and silver Inca artifacts today. When Atahuallpa was captured by Pizarro, every item made of gold or silver was gathered from every store throughout the empire and brought as a ransom for the emperor's life. Those artifacts were smelted into bullion and lost to history, but if Incas traded regularly with Mayans or Aztecs, we would find those artifacts throughout the entire Mesoamerica.

The Aztecs and the Mayas did know about each other. After all, they were right next to each other. But I don't think there is any evidence that one of those two civilizations met the Incas. Probably since the Incas were pretty far away.

Although I think that if there had been contact, the Mayas would've had the biggest chance since they traded more.

This article on Pre-Columbian Trade by Chester S. Chard would suggest they did. For instance:

There is no evidence that Maya traders themselves reached the highlands of Mexico; they traded their goods in the great commercial center of Xicalango, whence others carried them on. It is reported that the merchants of Xicalango furnished Cortez with fairly correct maps of the entire region to the south as far as Panama, which suggests extensive trade contacts.

There's a map on p.2 that shows established, sporadic, conjectured trade routes. I've only skimmed a few passages, but it seems pretty clear the Mayans were aware of and de facto trading with the other two. At the very least one could suggest it may have been like the Romans, who knew the Chinese existed and de facto traded with them through intermediaries.

Anecdotally I recollect also reading somewhere (possibly on this site or in a source reference from it) that the Spaniards' reputation had reached Florida long before they actually showed up, resulting in fairly hostile natives.

Aztecs did know about Mayas but the Mayan civilization was already dead. But of course, they did traded with its descendants - even prehistoric men traded with their neighbours.

And no direct contacts for the contemporary Incas civilization.

https://www.quora.com/Did-the-Aztecs-Mayas-and-Incas-know-about-each-other-Did-they-communicate-between-them

The only question remains open - if Incas or Mayas had sent some expedition to another civilization. Indirect contact surely existed, it existed even in the stone age across continents. AFAIK, no such expeditions are known.