The Red Devils have lost two of their opening three games for the first time since 1992-93, the latest of which saw them fall 3-0 at home to Tottenham Hotspur on Monday night.
Initial reports suggested that the United board had no intention of parting company with the former Chelsea boss, but the Daily Mail reports that chief executive Ed Woodward is now discussing the possibility of changing managers.
Woodward is reluctant to sack Mourinho, but a third successive defeat at the hands of Burnley at Turf Moor on Saturday could be the final straw for the club's hierarchy.
Players are reportedly already talking about the possibility of Zinedine Zidane taking over as manager, with the former Real Madrid boss thought to be interested in the post.
The report suggests that there is a similar feeling of inevitability around Mourinho's future as there was for Louis van Gaal's before his sacking in 2016.
In addition to United's on-field troubles, the early stages of the season have also been dogged by reports of unrest behind the scenes at Old Trafford.