That would be like having your own crystal ball.
I've got some GREAT news for you.
It is possible. Not 100%, but somewhere on the order of 75% to 85% accurate.
That's because music has FORM -- like the skeleton that holds your flesh, muscles, and skin up. If you had no bones -- no skeleton -- your flesh and all the other parts of you would fall in a heap on the floor. Not a pretty picture. But because you DO have a skeleton, you are able to walk around and pretty accurately predict which way your next step will take you.
It's the same in music. Music has FORM -- a skeleton to hold it up, hold it together. And that skeleton is made out of chords -- harmony -- the tonal center of the song or piece.In any given key you can play in, there are PRIMARY CHORDS -- chords that occur way more than other chords. They are like family members of that particular key.
At your house, let's say you have 3 people in your family -- your spouse, your child, and you. On the same block, but down the street a few houses, lives your cousin and her family.
At any given moment, who are the most likely people to be in your house?
President Obama? George Bush? Kyle Singler?
I don't think so.
It's possible, of course, but not too likely. If I had to guess, I would say it would be either you, your spouse, or your child. It might be your cousin down the street -- there's a much better chance of that than, say, Michael Phelps -- but my best odds would be to guess that the family members would be there.
It's the same way with chords. In any given key, there are 3 "family members" that are residents of that key -- the I chord, the IV chord, and the V chord. They are far and away the most likely chords to occur in any given key.
For example, if I am playing in the Key of C, and the first chord is the C chord and I have to guess what the next chord is, I would guess that it would be either the F chord or the G chord. Why? Because those are the other "family members". So we have narrowed the odds a great deal just by knowing who the members of the family are.
What chord comes next?
So how could I tell whether it should be F or G?
If the melody is a "B", then the chord is probably a G chord. Why? Because "B" is in the G chord, but is not in the F chord.
If the melody is a "A", than I would guess that the chord is F. Why? Because "A" is in the F chord, but is not in the G chord.
Does that mean that there are always just 3 chords in a song? No, but there are literally hundreds of songs that are made of just 3 chords.
For more complete information see "How To Predict Which Chord Comes Next In a Song"