The 22-year-old former Celtic youth player has made nine appearances for Rovers since moving to Prenton Park in November.
His solitary goal to date came during the 2-2 draw with Portsmouth last month.
"Michael has done well since he has been here so I'm pleased to be able to keep him for another month," manager Ronnie Moore said.
"With Jake Cassidy going back to Wolves and Jean-Louis Akpa Akpro not yet back from injury we're short of options up front so Michael being allowed to stay is good news for us.
"I'd like to thank (Bolton manager) Dougie Freedman for letting Michael stay with us."