Is there any place in the universe for two persons to feel each other's gravity?

Sorry, humans aren't sensitive enough to feel micronewtons of force between each other...no matter where in the universe they may be.

It would take 100 minutes for two 100 kg bodies to collide in deep space, initially being at rest 1 meter apart.

I know for certain the 100 minutes value, because in the past I've done the fancy calculus. Believe it or not, it cannot be accomplished to an exact solution, but requires numerical approximation.

I'm not exactly sure what you mean by the word "feel" but I assume you mean notice the effects of the gravity.

We don't notice the gravity of objects around us with the exception of the Earth of course, and the Moon and Sun on the tides. This is mostly due to the fact that other forces are so much stronger. Even though two people are pulled together by their mutual gravity, forces like friction are so overwhelming we never even notice.

If we were in a place void of friction, say floating in outer space, we would indeed notice.

Here's an example. If two 100kg astronauts were sleeping a meter apart on a space walk they would feel a mutual force of...

F = G*m1*m1/r^2 = 0.0000007N

As they got closer the force will get stronger, but we can still find the maximum time it would take for them to collide to be (we need some fancy calculus to get the actual answer)...

t = (2*x*m/F)^(1/2) = an hour or so

So believe it or not, if it weren't for friction, and other forces overwhelming gravity, we would notice each others gravitational pull rather quickly.

Any two objects with mass "feel" each others gravity no matter where in the universe you are. The Earths gravitational pull dominates here but that doesn't mean there is no gravitation between two bodies on it.