Filippo Inzaghi wants to keep on-loan Chelsea midfielder Marco van Ginkel at AC Milan for another season.
Liverpool defender Kolo Toure is close to agreeing an extension to his contract which expires next month.
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.