Wayne Rooney recently touched Bobby Charlton 249 goals for the Red Devils. Rooney soon will overtake the legendary footballer.
"I don't know the distances, really, but I think the ones that are close are players that left United already," the Portuguese said.
"So, especially in modern football I see it is really difficult. I don't know, who knows?
"Marcus, he is 19. If he plays Man United until the end of his career, maybe Marcus can do it but Rooney scored a lot of goals."
Marcus Rashford has been instrumental for the club since his debut in February 2016. He has already netted 14 times in a United shirt.
In the ongoing English Premier League season, the English youngster has scored 3 goals in 16 matches.
On Rashford's performance in the FA Cup match, Mourinho said: "I spoke with him at half-time. I told him that I don't care with the goals he missed in the first half because he had big responsibility in the way we were breaking their defensive line.
"He was playing so well for us. One more goal, one less goal - it doesn't change. But obviously for an attacking player to score a goal means happiness, means confidence, so it was good for him."