The 25-year-old moved to the Catalan club in 2013 and has been an integral part of their attack along with Lionel Messi and Luis Suarez. The forward has also committed his future to the Camp Nou outfit by signing an extension that will keep him at the club until 2021.
Neymar's father revealed last year that United were keen on securing his services. However, the Brazil international snubbed the opportunity and continued with his current employers.
Sport had earlier reported that Mourinho was keen on bringing Neymar to the Premier League and United will activate his €200m (£172.9m, $215.7m) release in order to beat competition from league rivals Chelsea and Paris Saint-Germain.
The latter two clubs are also believed to be interested in signing the former Santos star.
The same report claimed that United would offer Neymar a €25m-a-year deal – equivalent to €480,000-a-week. However, the former Chelsea manager played down the recent reports linking Neymar to the Red Devils and backed the forward to be the next superstar at Barcelona after Messi.
"It's speculation. I always try to be objective and pragmatic with clubs and to ask them what they can give me. To ask for Neymar is absurd," Mourinho told ESPN Brasil.
"A club like Barcelona can not and will not lose Neymar. Although Messi is still a young player with years ahead of him, he's almost 30, and Neymar will be the great player of Barcelona post-Messi. So much that I think it [trying to sign Neymar] is like trying to break into a safe, impossible."
Meanwhile, Neymar helped Brazil to become the first nation outside the hosts to seal a berth in the 2018 Fifa World Cup in Russia. The South American country achieved this feat by defeating Paraguay 3-0 in the World Cup qualifiers.