With two seasons left on his contract, which expires in 2019, United are prepared to extend his current deal, according to the Sun on Sunday.
The centre-back is battling back to fitness after Mourinho suggested he lacks the mental strength to play through his injuries.
Mourinho took a swipe at Smalling in the wake of United’s 3-1 victory over Swansea two weekends ago, but it later emerged that the 26-year-old was suffering from a broken toe and had played through the side’s 4-0 humiliation at Stamford Bridge last month with a pain-killing injection.
Smalling is allegedly close to match fitness as he looks to reclaim his spot in both the United and England outfit.
But with a United defence clearly struggling from a series of imbalances, it’s believed the side are also considering a sensational £25m bid for former player Michael Keane.
Mourinho’s men played with three left-backs when they welcomed Burnley to Old Trafford last month in a match in which Keane shined as the visitors kept a clean sheet.
After loan stints at Leicester, Derby and Burnley, the defender joined the Clarets from United in 2015 where he has moved from strength to strength.