Celtic boss Ronny Deila says keeping his best players will take priority over acquisitions in the transfer window.
Chelsea striker Fernando Torres is understood to be set for a return to Atletico Madrid, according to Sky sources.
The duo joined the Foxes at the start of November and will now remain with the npower Championship promotion challengers until January 2 2013.
Lingard played for United's Under-21 side on Monday and helped create Federico Macheda's goal in the 1-1 draw at Southampton before he was sent-off for handling the ball on the line. The 19-year-old has made four appearances for Leicester.
However, Keane's spell at the King Power Stadium was curtailed by a hamstring injury he sustained making his debut for the Foxes against Bolton on November 6.
The England Under-19 centre-back will link-up with Nigel Pearson's squad when he reaches full fitness.