WATCH MUTV club channel 24/7 via CONNECT | 2-week free trial
The England international, who has scored a career-best 27 goals in 44 games this campaign, is due to be out of contract at Old Trafford at the end of next season.
According to British publication the Daily Star, Rashford's United future is in limbo due to the ongoing sale of the club and his big wage demands.
However, the 25-year-old directly replied to the article on his personal Twitter page on Thursday (AEDT) to deny that is the case.
"Just before this one starts to do the rounds! It's complete nonsense," he said. "The club and make self [sic] have been respectful to one another, and that's how it will remain.
"My focus is purely on finishing as well as possible in the league and winning trophies."
Rashford added on Instagram: "Another non-story flying around about my advisors and me making demands. It's complete nonsense!
"My aim and the club's aims are to finish as high as possible in the league and to try and win a cup or two."
Rashford's goals tally this season has been bettered only by Kylian Mbappe (31) and Erling Haaland (42) among players across Europe's top five leagues.
He has spent eight seasons as part of United's first team since making his big breakthrough with two goals on his debut against Midtjylland in February 2016 as an 18-year-old.
Speaking last month, United manager Erik ten Hag confirmed the club are working on tying down the academy product to fresh terms.
"Of course [Rashford's new contract] is a priority," he said. "We are working on that. Just sit and wait. In the background. we are working hard."
Rashford missed England's two Euro 2024 qualifiers during the international window, but he is expected to be fit to feature against Newcastle United on Sunday.