Kilmarnock manager Steve Clarke is reportedly resigned to losing the 31-year-old when his current contract expires at the end of the season.
However, Rangers and Celtic aren’t the only Scottish clubs vying for his services, with Aberdeen and Hibernian keeping tabs on the former West Bromwich Albion man.
After impressing in the Scottish Premier League this season, there could be clubs in England considering making a move.
Signed on a free transfer in November 2017, Mulumbu has made 14 appearances for Killie in all competitions, scoring and creating five goals. He’s been a standout performer at Rugby Park.
The Daily Mail added that Mulumbu nearly left Kilmarnock to join Bordeaux in January before the deal between the two clubs broke down.
Joining Rangers would see Mulumbu adding more extra strength and stability to their midfield, but Champions League football with Celtic next season could lure him to Parkhead.
Based on his form this season, the 31-year-old will be a bargain buy for his next club.