From what we've seen on the show, it seems like TARDISes reproduce by budding, and don't have sexes. But of course the Doctor's TARDIS obviously has a female gender, so presumably, if another Time Lord had a similarly close relationship with their TARDIS, and treated it as male for centuries, there could be a TARDIS with male gender.
That being said, the Doctor's relationship with his TARDIS seems to be unusual, maybe even unique. The Rani and the Master certainly don't treat their TARDISes the way he does, and we've seen other characters who know about TARDISes mock the Doctor for his relationship with his.
In the novels, TARDISes can sexually reproduce, but it's implied that the male of the species is more like an insect drone, which has no function but to breed, not a usable TARDIS.
In the Faction Paradox spinoff series (which is deliberately not part of Doctor Who canon), the "bull engines" are only used for breeding Type 103 timeships from Compassion. Both earlier timeships and later ones can be male—in fact, Compassion's first offspring, Antipathy, is male.