The 27-year-old, who was close to leaving Old Trafford for Real Madrid in 2015, continues to be linked with a move to Los Blancos as part of a potential squad overhaul in the Spanish capital.
United boss Mourinho has said, however, that if the club want to challenge for silverware, they must keep hold of their best players.
"Do you think that a club that is trying to attract the best players is the club that is open to sell the best players? It makes no sense," the Portuguese boss told the Daily Mail.
"If you want to go to that level you have top attract the best players like we did with Alexis [Sanchez], [Nemanja] Matic and [Paul] Pogba and so on. And don't let our best players go."
De Gea, who moved to Manchester from Atletico Madrid for £18.9m in 2011, made his 300th appearance for United in a 2-0 win over Huddersfield Town earlier this month.