Versatile attacker McSheffrey has been an unused substitute in Birmingham's opening two Premier League games, while Bent has yet to be involved.
McLeish has discussed the situation with both players and is now waiting for clubs to make an offer before the close of the transfer window.
"I have spoken to Gary and Marcus and said that, by having to bring players in, we have to make sacrifices," said McLeish.
"We've told them that we will listen to offers."
McSheffrey joined Birmingham in a £4million move from Coventry three years ago and he has been linked with a return to his former club, while Crystal Palace and Sheffield United are also rumoured to be interested.
Much-travelled striker Bent recently vowed to fight for his place in McLeish's plans, but now looks to be on his way out after just 12 months at St Andrew's.