The 67-year-old has admitted that he would "love" to take over the club and eased concerns that they might be moved from Buffalo, but did warn that he would not pay over the odds if there was to be a bidding war.
"I'm going to give it a heavy shot. I would love to do it, and if I can do it, I'm keeping it in Buffalo. I live in New York, and it's easier for me to go to Buffalo than any other place. Where am I going to move it, some place on the other side of the country, where I have to travel for five hours?" Trump told Buffalo News.
"I have a track record that's pretty much unparalleled, but that doesn't mean that I pay stupid prices. Somebody could come out and bid through the roof for the Bills, something crazy.
"In which case, I'm sorry I can't do anything about that. You have to be sane. But maybe there's not going to be any other bids. You never know with these things."
Trump is estimated to be worth $3.9bn (£2.3bn) by Forbes magazine.