Currently at Marseille, the player’s contract runs out in the summer and a move away from France looks to be on the cards.
Rovers are reported to be one of three clubs who are interested with Fulham and newly promoted Birmingham City being the others.
According to reports in the French press, talks have already begun with the player's representative.
M'bami told Skysports: "I have made my mind up to move to another league.
"The Premier League will be my first choice but I am not focused only on the Premier League.
"I will make my destination clear in the next two weeks."