The Times is reporting that the Red Devils are now exploring the viability of a big-money deal to bring the 32-year-old back to the club he left in 2009.
Manchester United have already been locked in talks with Real Madrid over the potential signing of Alvaro Morata but it has now been suggested that Mourinho would rather bring Ronaldo to Old Trafford.
The story also claims that Real Madrid are working to try and convince Ronaldo to change his mind about leaving the club.
However, it also states that the Spanish club would be likely to accept a bid of around €150m (£131m) should the Portugal captain not change his mind.
Ronaldo’s future has been cast into doubt after he was accused of evading €14.7m (£13m) in tax by Spanish authorities.
Manchester United are on the lookout for a host of new players this summer but have thus far only completed the signing of defender Victor Lindelof from Benfica.
MORE: Man United latest news
MORE: Arsenal latest news
MORE: Chelsea latest news
MORE: Liverpool latest news