The Brazil international has long been linked with a switch to Old Trafford, with newspaper reports in February suggesting that United were ready to launch a £200 million bid.
And Neymar has now opened the door to a possible move to United, insisting that Mourinho's side are one of the teams that he admires and that "any player" would like to work with the Portuguese.
He told The Sun: "The Premier League is a championship that amazes me.
"I like the playing style and the teams. And who knows, someday, I would like to play at it, yes.
"And then you have high-level coaches like Mourinho and Guardiola. These are coaches with whom any player would like to work.
"In the Premier League you never know who is going to win or who will be champions, it is always a surprise.
"Leicester are very good. They had a great season last year, they were Premier League champions and therefore we need to respect them if we draw them in the Champions League."
Neymar has enjoyed a productive 2016-17 campaign with Barca so far, scoring 14 goals in all competitions.
The Catalan club are trailing Real Madrid in the Liga title race by two points, with Zinedine Zidane's side also having a game in hand over their fierce rivals.
Barca are also in the hunt for Champions League glory, with Neymar having set a record for assists in that particular competition, and will face Juventus in the quarter-finals following a miraculous comeback win over PSG.