The 20-year-old has been used twice from the bench in the Premier League and Champions League combined this term, while also being handed a rare start in the EFL Cup win over Swansea City in October.
United boss Mourinho is reluctant to offload Tuanzebe, but he concedes that the England Under-21s international risks seeing his growth stunted if he remains at Old Trafford when he could be getting valuable minutes elsewhere.
"Tuanzebe is a very good player who is not having many opportunities here," he told reporters. "But he is our player and he will be our player.
"There's no chance we'll give up on such a talented boy but we are thinking about a loan until the end of the season. We are delaying the decision until the end of the transfer window."
Tuanzebe, who has spent his entire youth and professional career to date at United, was handed four starts in the Premier League last term.