Two positively charge particle can attract each other but in extremely selective and peculiar conditions such as inside a nucleus.There is a very rare phenomenon seen inside the nucleus of an atom and between two proton( protons are positively charged bodis).The phenomenon is:There is an electrostatic repulsion between the protons in the nucleus. However, there is also an attraction due to another kind of force besides electromagnetism, namely the so-called "strong nuclear interaction". The attractive strong nuclear interaction inside the nuclei is 1-2 orders of magnitude stronger than the repulsive electrostatic interaction which is what keeps the nuclei together despite the repulsive electrostatic force.

Yes they can attract each other on certain conditions. . let's take an example take to parallel you charged conductor if the current moves in same direction then the two charges i.e electrons will attract but incase when the current flows in opposite direction then they will repel