The 33-year-old is reported to be in the north-west to complete a medical at the club before he signs a one-year contract.
The Uruguay international is a free agent after leaving Paris Saint-Germain, where he is the club’s record top scorer with 200 goals in 301 appearances for the Ligue 1 giants.
Mourinho orchestrated a humiliating 6-1 defeat on his former side at Old Trafford on Sunday that heaped the pressure on his replacement Ole Gunnar Solskjaer.
But, instead of reveling in the chaos he helped to create, Mourinho extended an olive branch to the Norwegian and says Cavani can help his side recover from the defeat.
‘The team is improving, they have good players, he bought lots of young players, they bought very good players,’ said Mourinho.
‘If it’s true that Cavani is coming, Cavani is one of the top strikers in the world.
‘Manchester United is Manchester United, it’s not this defeat that’s going to destroy them. I can imagine they are going to react like Manchester United always react.’
The Brazil international is set to sign a four-year deal with the option of a further 12 months.
But Untied fans will be desperate to see more faces arrive through the door, particularly a centre-back.
United have conceded 11 goals in their first three Premier League matches.