The forward was left out of United's squad for the derby victory at Manchester City at the weekend after manager Ruben Amorim appeared to question his application in training and has now suggested that he is open to leaving his boyhood club.
Rashford told football journalist Henry Winter: "For me, personally, I think I'm ready for a new challenge and the next steps.
"When I leave it's going to be 'no hard feelings'. If I know that a situation is already bad I'm not going to make it worse.
"I've seen how other players have left in the past and I don't want to be that person. When I leave I'll make a statement and it will be from me."
The England international found it "disheartening" to be left out of the squad for the derby but has vowed to continue working hard.
He said: "It's disheartening to be left out of a derby but it's happened, we won the game so let's move on.
"It's disappointing but I'm also someone as I've got older I can deal with setbacks. What am I going to do about it? Sit there and cry about it. Or do my best the next time I'm available."
In response, Amorim insists that United are a better team with Rashford in it and says his only aim is to help the player improve.
The coach said: "I just want to win and to help the team be better, so we are better with Marcus Rashford, and that's simple, we try different things to push Marcus to be at his best level that he's shown in the past.
"This kind of club needs big talent and he is a big talent so we just need him to perform at the highest level and that is my focus. I just want to help Marcus."