The England international has been linked with a potential move in the summer following a frustrating campaign.
Rashford was overlooked for Manchester United’s 3-2 win against Manchester City in the derby despite being a home grown talent.
The 20-year-old has only started 14 times in the Premier League this season, making a further 15 appearances from the bench.
The Red Devils forward was reported to be weighing up his future in the British media over the past week or so.
However, Manchester United would presumably be loathe to lose Rashford having aided his development.
Former Arsenal striker Wright doesn’t expect Rashford to leave Manchester United at the end of the 2017-18 season.
“The way Man United play, they should be a lot closer to Man City,” Wright told Sky Sports.
“Someone like Rashford didn’t get to play in the derby as a local lad. He has to be frustrated. I can’t see it happening [Rashford leaving].”
Rashford has scored 12 times in 43 games in all competitions this term. although most of those appearances have come from the bench.
The England international will be hope to secure a place in Gareth Southgate’s World Cup squad in the summer.
MORE: Man United latest news
MORE: Arsenal latest news
MORE: Chelsea latest news
MORE: Liverpool latest news