The Poland international was a mooted target for the Red Devils throughout the summer as Louis van Gaal searched for fresh defensive options.
However, a move failed to materialise, and Glik has since remained in Turin.
And now reports from talkSPORT, via Tuttosport, claim that the 27-year-old is on the verge of agreeing fresh terms with the Serie A side, which will effectively end any hope of a rumoured January move to Old Trafford.
Glik is set to double his current salary to around £20,000-per-week with an announcement expected later this week.
The classy defender played alongside current United right-back Matteo Darmian before the Italy international moved to the Theatre of Dreams over the summer.