The agent, Winnie Haatrecht, also said that Babel would consider a move to St Andrews should a fee be agreed between the two club's for the Holland international forward.
"We know that Liverpool seriously thinks about the offer from Birmingham, we would consider a deal if both clubs come to an agreement," Haatrecht told De Telegraaf.
"In general Ryan wants to succeed at Liverpool but if the people at Anfield conclude it's better he leaves then we have to think about the next chapter in his career.
"We will look then to the team, the perspectives of the club and Ryan, as well as a meeting with the manager.
"I have sent all interested clubs to Liverpool, finally five or six clubs contacted the club.
"None of them came to an agreement with Liverpool."