Lundstram had been linked with a move to the Championship, with Middlesbrough one of the clubs said to be interested in him.
The midfielder arrived at Ibrox at the beginning of the season from Championship side Sheffield United but his time at the club has not been a bed of roses.
Lundstram received criticism for his early season performances and transfer talk began swirling about a potential departure.
However, the Gers are not intent on him moving him out this window and he will see out at least this season at Ibrox.
Lundstram has made 26 appearances in all competitions this season but his playing-time has been reduced recently.
Rangers are hoping to sign Juventus outcast Aaron Ramsey toady and he could provide more competition for Lundstram.
Lundstram’s contract with the Gers runs until the summer of 2024 and it remains to be seen whether transfer speculation erupts again in the summer.