The Red Devils ended their 2016/17 season on a high note by winning the Europa League as they saw off Ajax 2-0 in the final. The English club secured a place in the next season's Champions League group stages, despite finishing 6th in the league table.
Griezmann has been heavily linked with a move to United, while he has also attracted interest from other top clubs in Europe. The France international further fueled the speculation after claiming the possibility of his move to United is "six out of ten".
The former Real Madrid and Chelsea manager confirmed that he has already made United executive vice-chairman Ed Woodward aware of his summer transfer targets. However, the Portuguese tactician refused to give out any details on the rumours suggesting that his side are interested in signing Griezmann.
"I do not want to talk about Griezmann because that would be disrespectful to his club, Atletico. Just how I do not like others talking about by my players, I'm not going to talk about Antoine either," Mourinho told beIN Sports, as quoted by Marca.
Griezmann has a €100m (£85m, $110m) release clause in his current contract with the Spanish capital club. It is widely believed that United are still in the race to secure his services as the Telegraph reports the 26-year-old still remains Mourinho's key target for the summer transfer window.
Meanwhile, another player linked with a move to United is AS Monaco's Bernardo Silva. According to the French publication Le 10 Sport, the Portuguese international is wanted by the 20-time English champions.
Mourinho says the Red Devils are unlikely to make an approach for the 22-year-old, but admitted that "good players are always welcome" to Old Trafford.
"I think not. Honestly, I think not. But you never know. Good players are always welcome," United manager told Sport TV, as quoted by Goal.com.