Are Christians called to forgive Unbelievers?

In addition to the above The entire purpose of Jesus death and resurrection was to forgive the un-forgiven. You refer to them as non believers, but it must be remembered that the Gentile Nations were not believers, and yet Jesus himself sent Paul to the Gentile nations:

Acts 9:5 and 6 NKJV And he said, "Who are You, Lord?" Then the Lord said, "I am Jesus, whom you are persecuting. It is hard for you to kick against the goads." 6 So he, trembling and astonished, said, "Lord, what do You want me to do?" Then the Lord said to him, "Arise and go into the city, and you will be told what you must do."

Acts 13:47 NKJV For so the Lord has commanded us: 'I HAVE SET YOU AS A LIGHT TO THE GENTILES, THAT YOU SHOULD BE FOR SALVATION TO THE ENDS OF THE EARTH.' "

We also have the prophesy of Simeon at Jesus dedication:

Luke 2:25 through 35 NKJV And behold, there was a man in Jerusalem whose name was Simeon, and this man was just and devout, waiting for the Consolation of Israel, and the Holy Spirit was upon him. 26 And it had been revealed to him by the Holy Spirit that he would not see death before he had seen the Lord's Christ. 27 So he came by the Spirit into the temple. And when the parents brought in the Child Jesus, to do for Him according to the custom of the law, 28 he took Him up in his arms and blessed God and said: 29 "Lord, now You are letting Your servant depart in peace, According to Your word; 30 For my eyes have seen Your salvation 31 Which You have prepared before the face of all peoples, 32 A light to bring revelation to the Gentiles, And the glory of Your people Israel." 33 And Joseph and His mother marveled at those things which were spoken of Him. 34 Then Simeon blessed them, and said to Mary His mother, "Behold, this Child is destined for the fall and rising of many in Israel, and for a sign which will be spoken against 35 (yes, a sword will pierce through your own soul also), that the thoughts of many hearts may be revealed."

We also have the words of Jesus himself:

John 10:14 through 16 NKJV I am the good shepherd; and I know My sheep, and am known by My own. 15 As the Father knows Me, even so I know the Father; and I lay down My life for the sheep. 16 And other sheep I have which are not of this fold; them also I must bring, and they will hear My voice; and there will be one flock and one shepherd.

Matthew 6:9 through 15 In this manner, therefore, pray: Our Father in heaven, Hallowed be Your name. 10 Your kingdom come. Your will be done On earth as it is in heaven. 11 Give us this day our daily bread. 12 And forgive us our debts, As we forgive our debtors. 13 And do not lead us into temptation, But deliver us from the evil one. For Yours is the kingdom and the power and the glory forever. Amen. 14 "For if you forgive men their trespasses, your heavenly Father will also forgive you. 15 But if you do not forgive men their trespasses, neither will your Father forgive your trespasses.

And finally we have Jesus saying:

Matthew 5:43 through 48 NKJV "You have heard that it was said, 'YOU SHALL LOVE YOUR NEIGHBOR and hate your enemy.' 44 But I say to you, love your enemies, bless those who curse you, do good to those who hate you, and pray for those who spitefully use you and persecute you, 45 that you may be sons of your Father in heaven; for He makes His sun rise on the evil and on the good, and sends rain on the just and on the unjust. 46 For if you love those who love you, what reward have you? Do not even the tax collectors do the same? 47 And if you greet your brethren only, what do you do more than others? Do not even the tax collectors do so? 48 Therefore you shall be perfect, just as your Father in heaven is perfect.

It is not possible to love others as yourself and not forgive them for their wrongs.

Last of all remember that Jesus said: Therefore you shall be perfect, just as your Father in heaven is perfect. And that perfect God in his perfect love sent Jesus:

John 3:16 and 17 For God so loved the world that He gave His only begotten Son, that whoever believes in Him should not perish but have everlasting life. 17 For God did not send His Son into the world to condemn the world, but that the world through Him might be saved.

So if God loves us so much as to do that, is his asking us to forgive others that big of a thing?

I think it's as simple as the Bible states that we should not judge others. Therefore we have no reason to forgive them as it's not our job to judge them:

Matthew 7 NIV

Judging Others 7 “Do not judge, or you too will be judged. 2 For in the same way you judge others, you will be judged, and with the measure you use, it will be measured to you.

3 “Why do you look at the speck of sawdust in your brother’s eye and pay no attention to the plank in your own eye? 4 How can you say to your brother, ‘Let me take the speck out of your eye,’ when all the time there is a plank in your own eye? 5 You hypocrite, first take the plank out of your own eye, and then you will see clearly to remove the speck from your brother’s eye.

6 “Do not give dogs what is sacred; do not throw your pearls to pigs. If you do, they may trample them under their feet, and turn and tear you to pieces.

However, is there any verse concerning how we are to forgive non believers ?

"Forgiveness" concerns the restoration of relationship.

If a brother in Christ asks for forgiveness, we are to grant it.

Paul gives an example of one who was disciplined by the church in Corinth and had repented and wanted to rejoin in fellowship.

2 Corinthians 2:7 So that contrariwise ye ought rather to forgive him, and comfort him, lest perhaps such a one should be swallowed up with overmuch sorrow.

As real relationship with the unsaved is not possible, there is a real limit as to what forgiveness could accomplish.

2 Corinthians 6:14-15 Be ye not unequally yoked together with unbelievers: for what fellowship hath righteousness with unrighteousness? and what communion hath light with darkness? And what concord hath Christ with Belial? or what part hath he that believeth with an infidel?

However, we are to work as well as we can with them.

Romans 12:18 If it be possible, as much as lieth in you, live peaceably with all men.