The Daily Mail says United consider it increasingly likely they will re-sign injured centre-forward Ibrahimovic.
A deal could be completed as early as this month.
Ibrahimovic, 35, is out until the new year with a serious knee ligament injury which he suffered during United's Europa League tie with Anderlecht last April, but manager Jose Mourinho is keen to have him enlisted for the knockout stages of the Champions League.
The terms of his proposed short-term contract will be greatly reduced from last season when he signed for PSG.
But with Ibrahimovic's recovery thought to be progressing well, United are sure he will be part of their plans later in the season and are prepared to show willing by offering terms sooner rather than later.