The Daily Mail says Ed Woodward and Mourinho shared a "positive" conversation in the aftermath of United's 3-0 defeat by Tottenham at Old Trafford on Monday night.
The pair then held a long chat which focused on what was an encouraging first-half performance from United before Spurs took over after the break.
Sections of United's board have voiced concerns over what has been a disappointing start to the season.
However, Mourinho retains the backing of the club's top brass who believe he can turn things around. They are also encouraged by the performance in the first half, which saw a vibrant United waste a number of chances.
And that was clear when Woodward spoke with the manager following the final whistle. Both men were seen engaged a "lengthier than normal" conversation which appeared to be "positive" according to witnesses.