The Wales global has been linked with a potential switch to Old Trafford from the Champions League holders in the current transfer window.
Perisic, 28, is keen on moving to Old Trafford but the Red Devils are unwilling to meet Inter's £50million valuation of the Croatia winger.
After completing the signings of Romelu Lukaku, Nemanja Matic and Victor Lindelof, United fans will be wondering if their summer spending is already over.
Inter winger Ivan Perisic has always been linked with a move to Old Trafford, while Paris Saint-Germain full-back Serge Aurier is also a reported target, and Mourinho admits that he hopes to welcome one more new face to the club before August 31. "We don't want to sell him, he is a very important player for us".More news: Bowled over by Mithali Raj & Co's show, city girls bat for cricket
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Mourinho insisted that Martial, who joined the club from Monaco two years ago in a deal worth a total £58million, remains a big part of his attacking options looking forward to the coming season. But the delay over the move highlights the struggles Mourinho's side have encountered getting deals over the line this summer.
Paris St Germain right-back Serge Aurier is another player who has been linked with a move to United but sources close to the club have dismissed any talks with the player.
Jose Mourinho added to the club's rich history of silverware last season by collecting the EFL Cup and Europa League but United limped to a disappointing sixth-place finish in the top flight. The England worldwide was heavily criticised by his manager last season for his lack of fitness and application but those fears are understood to have been dampened during an impressive pre-season.