Martial has enjoyed a mixed time of things since joining United from Monaco in 2015 as he excelled during his debut campaign when he scored 17 goals under former boss Louis van Gaal.
Reports have claimed that Arsenal have already seen an opening bid turned down for the 2015 European Golden Boy award victor but they remain interested in signing the France worldwide.
Manchester Evening News report that Martial "is understood to be 'very content' at United after making an electric start to his second season".
The newspaper says the French global is happy at Old Trafford and he seems to be winning over Mourinho after the United boss heaped praise on the attacker late last month.
The France global has started only once in the Premier League this season but has amassed five goals in all competitions, and the Mail reports that Barcelona "believe he is good enough" to succeed for them.
Arsenal were linked with a January move for Martial over the weekend as Gunners manager Arsene Wenger looks to replace Alexis Sanchez, who is out of contract at the end of the season.
"I see a great improvement in the person, in the mood, in the face, in the body language", Mourinho said of Martial last month. If you want just a word, in the happiness. He starts matches, he tries to do well.