Rashford, 19, has dazzled since bursting onto the scene in 2016.
Despite his relative youth, the England international is already an established star in the United first-team.
Barca are already planning for the future having signed Ousmane Dembele from Borussia Dortmund on Friday.
And Spanish new outlet Don Balon reckon Rashford is being targeted next.
Securing his signature certainly won’t be cheap, though.
“Man Utd star Marcus Rashford is wanted by Barcelona”
Don Balon say he could cost the Catalans an eye-watering £185m.
Speaking earlier this month, pundit Steve Nicol claimed Rashford would be the game changer for United this season – not new boy Romelu Lukaku.
“I know they’ve signed Lukaku to put the ball in the back of the net, but I think if they’re to be successful the key will be Rashford,” Nicol told ESPN FC.
“I think Lukaku will take a lot of attention away and if Rashford can play in and around Lukaku, then he can score goals. If he plays wide I think he’s effective.
“A successful Man United for me means Rashford (playing well).
“I think he’s got all the qualities, he hasn’t quite managed to put it together.
“I think this season is a big season for him.”
United defeated Leicester 2-0 at Old Trafford yesterday to maintain their unbeaten start to the season.