The Mexico international has turned heads in the Eredivisie, and Richard Fay of the Manchester Evening News noted that United have scouted him extensively.
Speaking to TalkSport's Universe Premier on Tuesday (h/t Fay), the attacker said he was grateful for the speculation linking him to the Old Trafford giants:
"I liked Manchester United a lot [as a child]. In Spain my favourite team is Barcelona.
"It's nice English papers talk nicely about me. It's special. Personally I say thanks for the nice words. I always try to improve and give something extra. I will keep on improving."
"I hope that God, some day, gives me a shot at playing in the Premier League. I like it very much.
I think the Premier League is great. I think that it would be fabulous to play with any of the clubs, but I would love to play for one of the big clubs. I hope that God gives me the chance."
The Mexican joined the Dutch club from Pachuca in 2017 after being linked with United.
Lozano has been a huge success at the Philips Stadion, and a move to a bigger team should materialise soon.
The winger, who can feature on either side, has scored nine goals and provided five assists in only 15 Eredivisie and Champions League games this term, making him one of the country's hottest properties.
United previously signed Ruud van Nistelrooy, Jaap Stam, Park Ji-Sung and Memphis Depay from PSV.
Football.London correspondent Alasdair Gold tweeted during PSV's first game with Spurs in Champions League Group B in October that he's not impressed with the winger's willingness to go to ground:
Lozano might find life tough in the Premier League, with successful Eredivisie stars often being swallowed up by the intensity of English football.
However, the Mexican's creativity would be appreciated at the Theatre of Dreams. United fans often take wingers to their hearts, and Lozano could be a very popular signing.
Mourinho's attack has started to display rising form after United beat Juventus 2-1 in Turin in the Champions League, but the coach would jump at the chance to add a player who could deliver crosses with precision.