What if we throw two solid objects parallel in space? Do those two objects have any chance to collide with each other? What will happen if just throw two solid objects (for example, solid footballs) parallel in outer space and those two objects are floating and going far away in the universe.

So is there any possibility in which those two football-size solid objects can collide with each other, or will they will float parallel for an infinite amount of time in the universe?

I'm considering gravity also, and I find that other stars's and planets's
gravitational pull can pull them into their gravitational fields and change their direction.

But what if those two objects will never get destroyed by luck? Could those will collide each other?
It all depends on the direction you "throw them" and the space-time they find themselves in.

Case 1 - in a perfectly empty universe (other than your footballs) the two would eventually collide. It doesn't matter what initial velocity you give them. The only thing that matters is there separation and their mass. You can just use Newtonian gravity to compute the two footballs' acceleration toward one another -- and hence the time for them to collide.

Such an 'empty' universe as above is called a Minkowsky space-time.

If you put these footballs on a trajectory into our real universe, well we know that space-time is curved by the matter/energy (just energy density in general) that occupies it. Hence a trajectory that starts out parallel will invariably end up "not parallel". The balls will either collide or diverge depending on the geometry of the space-time they find themselves in. The "geometry of the space-time" is (again) completely dependent on the distribution of "stuff" (matter/energy) in the universe as related to the location of the footballs.

In short, the footballs will follow the geometry of the space-time they find themselves in. That geometry (in our real universe) means they will not remain on parallel paths.