And Mundo Deportivo say the Spanish giants could also offer winger Malcom to United in their attempts to sign Rashford.
Barcelona signed Coutinho from Liverpool in January 2018 for a fee that could reach £142million and paid £36.5m for Malcom from Roma that summer.
Brazil international Coutinho has struggled at times at the Nou Camp and has since been linked with a move back to the Premier League.
Manchester United are keen on him, as are Chelsea and former club Liverpool.
Manchester United star Marcus Rashford is wanted by Barcelona (Image: GETTY)
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Malcom has sparked less interest from English football, netting only three times in 15 appearances for Ernesto Valverde’s side this season.
United will fight to keep hold of Rashford, who at 21 is one of the game’s brightest talents.
And Spanish football expert Guillem Balague has poured cold water on the transfer, insisting Coutinho will be staying at Barcelona.
He said: “Barcelona don’t want to sell. This story has come from nowhere.
“There is no intention to sell Coutinho.
Barcelona playmaker Philippe Coutinho has been linked with a return to the Premier League (Image: GETTY)
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“Coutinho has to improve certainly, we haven’t seen his best version.
“Barcelona don’t want to sell, but I don’t think it's (the speculation) just the media. Behind the scenes I think there’s a real push (from Barcelona) to keep him attractive to the Premier League in case they decide to sell.
“There’s been meetings with the representatives and Barcelona have come to the conclusion that moving forward he’s very important to the side.
“Now have Barcelona said that because it’s an important part of the season and they want to see the best possible Coutinho? I don’t know.
“Because what we are hearing is that the club are saying he is not for sale.”