Mourinho is keen on centre-backs Harry Maguire and Yerry Mina, who both starred at the World Cup and who both are a danger from set-pieces.
Wright believes the fact they are strong in the air and a goal threat is key behind United wanting them – despite their relatively quick rise to the top.
United have just days left to get a deal done with the window closing on Thursday at 5pm.
“Yerry Mina does have strengths – that aerial ability. Jose Mourinho does like physically imposing players throughout his career and that’s certainly the case at Manchester United as well,” he told the Transfer Talk podcast.
“Eight of his 11 signings have been 6ft tall and Mina is 6ft 5ins. He certainly ticks that box and he’s great from set pieces as well.”
“The interest in Maguire as well suggests it’s an area Mourinho is looking to strengthen.
“They have scored 21 goals from corners and free-kicks since his appointment. It may sound like a lot but it only puts them 12th among Premier League sides with goals from set pieces.”
Mina, 23, shone at the World Cup for Colombia but Wright has warned United of buying him just after a good three games.
“I think he’s a risk. It’s only six months since Barca paid £10m for him. They only played him four La Liga games in that time,” he said.
“One of those games he started was a loss to Levante when he struggled with the pace and movement around him.
“I think it really does go to show what a good World Cup can do for a player. Three goals in three games in Russia and suddenly he’s a Manchester United target and suddenly Barca are looking to make a massive profit on him which is kind of incredible.
“The World Cup is just a small sample size those three games. Any player can have a good three games. It’s just a huge risk.”