What you are essentially trying to do with this is turn two species into one species. The question then becomes: what is the goal?
an additional, new, species: are they trying to make a new species with combined properties of the old ones? If so, this would presumably be to serve some purpose. In these cases, however, they probably wouldn't want a proper, breedable, new species because they could lose control over their creations in the wild. So they would prefer unbreedable hybrids.
eradication of existing species: are the people of your story, in some round-about, double-think, politically correct way, attempting to eradicate one, or both, species from the environment? This could lead to a very sinister story (which might be great!).
Regardless, if you're goal is genetic similiarity (especially without any genetic manipulation) then, at the very least, you must ensure each species has the same number of chromosomes (note: even humans and chimps don't have the same number of chromosomes, so this is not a given).
However, comparing the individuals of each species for genetic similarity is likely an exercise in futility even if they're close to each other (and you'd want them close to start or you make the entire process far more difficult and take much more time).
I tried several times to give a concise answer from here and always end up writing a book, so here it goes again. Briefly, what you have to consider is:
(a) that the species have gross genetic differences already
(b) you're trying to separate relatively small differences (the individuals in a species) from very large, coarse differences (between the two species)
(c) it's not as straightforward as looking at the genes because the 'junk' DNA between genes is actually crucial for gene expression and function and therefore, must also be considered
(d) you're also fighting against random mutations (about 1 mutation/1,000,000 cell divisions) that could move your project backward or forward.
There are so many issues that would make this an exercise in futility that you would have to have very bored, very long-lived, creatures that would even contemplate attempting this.
However, I suppose, technically, it could eventually be done.