Currently on-loan at Aston Villa, Rashford can be signed permanently for £40m.
Villa are keen, but Rashford would prefer to join a Champions League participant next season.
And transfer expert Fabrizio Romano is reporting Barca remain interested in the England international, reporting on his YouTube channel: "At Barcelona, they still believe that Marcus Rashford could be an option for the summer transfer market. They believe, at Barcelona, that Rashford might be available on the market.
"Barcelona believe he could be a good solution because he can play as a number nine, he can play on the wing so he can help in several positions and he is a player who is appreciated by those at Barcelona.
"They wanted Rashford in January but it didn’t happen because Ansu Fati didn’t leave so because of financial fair play it was not possible to make a deal - but Marcus Rashford remains in the list of Barcelona. So if Rashford is not remaining at Aston Villa, we will see what happens. He is under consideration."