Bridge, 29, is out of action after undergoing a hernia operation.
According to The Sun, Eastlands boss Mancini has urged him to think carefully about doing a U-turn as he believes the Three Lions have a golden chance of lifting the World Cup in South Africa this summer.
"When he comes back to training I'll speak with him - I hope he will play in the World Cup," Mancini was quoted, as saying.
"It's important for a player to take the chance to play in a World Cup. You don't get many chances in your life to do that. I hope for Capello and England that Wayne can change his mind," he added.
Bridge is sidelined until mid-April.