Questions over the Spaniard's Anfield future intensified when the Merseyside outfit completed the capture of shot-stopper Simon Mignolet from Sunderland.
"I'd be very surprised if both of them were there on September 1," the Daily Star quotes Molby as saying. "In the first three or four years Pepe was here he was as good as the club's ever had.
"He hasn't quite been the same in the last couple of years but I think he's a great keeper. Possibly the time has come for him to move on."
Reina, who has been linked with a switch to Barcelona, joined Liverpool from Villarreal in 2005.