But Mourinho has decided to make the first move to try and beat the rest of the suitors by making a bid - and the Red Devils could have an advantage over the situation following the signing of Lindelof.
According to Spanish outlet Mundo Deportivo, the Portuguese boss has bid for compatriot Semedo.
The Catalan manager is looking to bring the hot prospect to the Etihad this summer, in order to strengthen the right-back position at Man City.
Semedo, 23, has been tipped to leave the Portuguese giants during the summer transfer window after having garnered a reputation as one of the most promising right-backs around Europe.
Hector Bellerin is still being heavily linked with Barcelona but may be hard to prise away from Arsenal.
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"Mourinho wants me, he has wanted me for a long time and I am an admirer of his work".
Benfica expect to raise at least 40 million euros from Semedo and are likely to reject this 35 million euro offer.
"I see this happening because Arsenal need centre-halves".
Now on duty with Portugal at the Confederations Cup in Russian Federation, the right-back has made four worldwide appearances. He was an unused substitute for the 2-2 draw with Mexico yesterday.
United are expected to mount a serious title challenge after winning the EFL Cup and Europa League last term.