Mulumbu joined Celtic in the summer of 2018 on a free transfer after leaving Scottish Premiership rivals Kilmarnock at the end of the 2017-18 campaign.
Celtic manager Rodgers has suggested that the DR Congo international could go out on loan this month.
Rodgers told The Scottish Sun: “Youssouff is at the age where he needs to play really.
"He came in as a support player to the team but he’s at the age really where he needs to play in the next part of the season so he’ll probably go out on loan too.”
Mulumbu played well for Kilmarnock last season, but it was always going to be hard for the former West Bromwich Albion midfielder to establish himself in the Celtic starting lineup this season.
The 31-year-old is a good midfielder, and the former Norwich City star is unlikely to have any problem in find a club to join on loan for the second half of the season.
The Scottish Premiership is on a mid-season winter break at the moment.