Kent revealed over the summer that he was diagnosed at the end of 2013 with throat and tongue cancer, but that after treatment he shows no remaining sign of it.
The MP for Ontario's Thornhill riding said he would ask Health Minister Rona Ambrose to consider federal funding to help the provinces provide vaccinations to teenage boys for free.
Right now, girls between ages nine and 13 can receive a free HPV immunization no matter where they live. But only two provinces offer boys the same option, as most governments bank on so-called herd immunity.
Kent says Ambrose spoke to provincial and territorial health ministers recently "and found that there was general agreement that in principle" that each jurisdiction wants to provide the vaccine when they "can find the funding."
Kent said he can't reveal federal budget plans, but that Ambrose agrees there should be federal funding to provide the vaccine for free.
But the former environment minister said he will ask Oliver to include such funding in the next budget.
"When we get to the detail of the pre-budget consultations, I'll be making a recommendation, yes," Kent said.
The Canadian Medical Association, a number of provincial medical authorities and the National Advisory Committee on Immunization have all recommended HPV vaccination for pre-adolescent boys as well as for girls, he added.