Darren Bent insisted he had to leave Aston Villa after too many "slaps in the face".
Brighton defender Greg Halford has agreed to extend his loan deal from Nottingham Forest until the New Year.
After spending 10 years at Wanderers, the 36-year-old is currently weighing up his next move and the Championship club have emerged as firm favourites to land him.
However, Sheffield United fan Davies says it would not bother him if their arch rivals made a bid for him.
He told the Sunday People: "When I was younger I supported United but my father supported Wednesday, so we were pretty split as a family.
"Everyone's different, of course, but if it's a club that appeals to you - the manager, the fans and the team - I would have to look at it. If an offer does come then I'll give it serious consideration."
Davies has also been linked with Blackpool, Brentford and Millwall after a move to MLS side Toronto fell through.
However, the experienced striker has not ruled out a move across the pond and he added: "There's no massive rush on my front. I just want to make sure it's right.
"There are a lot of ambitious young managers around so if it was the right club, the right manager and the right area, I wouldn't rule it out."