Serie A giants Juventus are monitoring the market for defensive reinforcements after Dani Alves decided to leave the club after just a year in Turin.
Juve are also planning for life after Alex Sandro, with the Brazilian full back closing in on a move to Premier League champions Chelsea worth £60million.
Inter have also been linked with Italy international Darmian, who joined United in 2015, but Mourinho is keen to keep the defender in his ranks over the summer.
ESPN say the Portuguese boss would prefer not to lose Darmian as he sees the 27-year-old as a valuable and versatile member of his squad.
While he failed to earn a regular starting place at Old Trafford last season, Darmian enjoyed a productive run towards the end of the campaign, starring in the club’s Europa League triumph over Ajax in May.
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Reports from last month suggested Darmian was keen to secure a summer departure, knowing regular football is necessary to secure a spot in Italy’s squad for the 2018 World Cup.