The German was initially banished from the first team by Mourinho but managed to forge his way back into the fold prior to the Christmas period.
It was reported earlier this season that Schweinsteiger was subject to interest from MLS side Chicago Fire, alongside other overseas clubs.
And according to Turkish media outlet HTSPOR, Mourinho has personally told Advocaat that Schweinsteiger was available during the January transfer period.
Schweinsteiger, back when he was vehemently exiled by Mourinho, released a statement out of the blue, telling Man United fans that, firstly, he was committed to the cause at Old Trafford and, secondly, that United would be the last European club he plays for.
A proposed move to Fenerbahce, therefore, seems unlikely, and with the transfer window nearly over Schweinsteiger appears to be staying put. Morgan Schneiderlin and Memphis Depay were both swiftly moved on by Mourinho, but no such noise has surrounded the German over the past few weeks, despite his notable lack of game time at Old Trafford this season.
United fans will be curious to see whether Schweinsteiger remains at the club until at least the summer or chooses to move elsewhere over the next week.