Martial could sign a new contract worth £130,000-a-week that would see him stay with the club for the next five years.
According to the 'Daily Mail' Martial may be signing a new contract now, because he believes that Mourinho's leadership will not be around for much longer.
There has been talk that Mourinho could be sacked following his poor start to the season, and public negativity.
Martial could be looking to make the long-term deal before United bring in a new manager.
It is a clear U-turn from earlier in the transfer window, when the 22-year-old's agent confirmed that Martial had rejected a new contract and wanted to leave.
Martial still has 12 months left of his £90,000-a-week contract and knows that United will trigger a 12-month extension if no new deal is agreed.
If chief executive Ed Woodward were able to get Martial on another long-term deal, it would be a huge success for him, after heading up an unimpressive transfer window in summer.
Mourinho had wanted to sell the winger in order to generate funds, after becoming irritated by his playing style and attitude.