The Black Cats' goalscoring potential looks to have been severely dented by Bent's £24 million move to Aston Villa, with only two players in the squad - Asamoah Gyan and Danny Welbeck - having netted more than one league goal.
Spurs striker Keane, whose move to Birmingham fell through on Monday, is a proven scorer - but Quinn, a former international team-mate of Keane, says the club are looking for a more physically imposing player.
The chairman's revelation will do nothing to dampen rumours of a bid for Cardiff's Jay Bothroyd, who the Welsh side could cash in on before his contract expires in the summer.
"What we are looking for to help [Asamoah] Gyan and Danny Welbeck along is probably a physical presence," Quinn told Kildare TV. "Robbie works well off a big physical player, but we don't have that now. Robbie doesn't quite suit us now."