The Red Devils are in second place in the Premier League table and 16 points adrift of the runaway leaders with eight games to go.
Manchester United are in a good position to wrap up a Champions League spot thanks to their eight point lead over fifth-placed Chelsea FC.
Mourinho has signed eight players since taking over the reins at Old Trafford from Dutch head coach Louis van Gaal in May 2016.
The Portuguese coach’s additions include world-class talents such as Paul Pogba, Alexis Sanchez, Nemanja Matic and Romelu Lukaku.
However, the Red Devils haven’t made sufficient progress in pursuit of their first Premier League title since 2013.
Former Manchester United defender May believes Mourinho still needs up to five new players in the summer transfer window to get the Red Devils squad to an acceptable level.
“Given time the team will be built around him [Paul Pogba],” May told 888sport.
“The manager is still four or five players away from getting where he wants to get to. He likes a big man up front and now he has Lukaku.
“He likes a holding midfielder and now he has Matic. I’m sure in the summer he’ll go again and hopefully from that United can get closer to where City are.”
Manchester United finished in sixth place in the Premier League table last term in Mourinho’s first season in charge.
The Red Devils won the Europa League and the League Cup under the Portuguese head coach.
Manchester United signed Chile international Alexis Sanchez in a swap deal from Arsenal in the January transfer window.
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