Mourinho will enter the transfer market for a big-name stopper if De Gea goes and he believes Romero should remain as a back-up choice.
Jan Oblak reportedly has a £85m buyout clause in his contract with Atletico Madrid.
In De Gea's absence, Romero showed all of his qualities against the Saints on Wednesday evening as he was awarded the Man of the Match award for his performance, which included a penalty save.
What is unclear at this stage though is who will replace him at Old Trafford, as The Daily Star report that while United will collect £60m from his sale, they'll use £40m of that to prise Oblak away from Atletico.
This a vast improvement on the £25million fee they agreed with Manchester United just two years ago, when De Gea's transfer to the Bernabeu broke down at the last moment of the 2015 summer transfer window.
De Gea could have now played his last game for United with Mourinho set to put a third team out on Sunday for their final league game against Crystal Palace.
De Gea has always been linked with a move to Real Madrid, but speculation has ramped up in recent weeks to suggest that this time round it could genuinely happen.
Big names such as Jan Oblak have been linked as possible targets for the Red Devils ahead of the summer, but it now looks like Romero has earned his chance to take the number one spot, according to The Sun.
He has already said he will give 20-year-old Joel Castro his first start for the club in goal as he saves both his goalkeepers for Wednesday's Europa League Final.