The Hoops boss has seen his side drop 12 points behind Old Firm rivals Rangers in the race for the Scottish Premier League title but Wales international Ledley says everyone in the playing group is right behind their gaffer.
"We want him to stay," said Ledley. "He's a great manager and we all want to try to win things for him and ourselves.
"It's hard when he's getting criticism when he's brought all us players in.
"We just have to keep working hard and try to get back on track. He is one of the greatest managers I have worked with and we want to keep him here.
"I think he still believes in us as players. We want to keep him here because he is a great manager and everyone believes in him."