Ole Gunnar Solskjaer is determined to improve his squad after a sixth-placed Premier League finish for United.
The Red Devils have been linked with a move for Coutinho, who previously shone in England with Liverpool.
The Reds have also been linked with a move for the Brazilian, who is currently playing in the Copa America.
And the 27-year-old has refused to rule out a departure from the Nou Camp later this summer.
“I don’t know if I will continue at Barcelona,” Coutinho said.
“Nobody knows about the future, and right now I am focused on playing with my [national] team [at the Copa America].”
Coutinho has struggled at Barcelona, though he has scored 32 goals in 76 fixtures.
He has regularly found himself left out of a Barca team though that features Lionel Messi and Luis Suarez.
And South American football expert Tim Vickery believes a return to the Premier League would suit Coutinho.
“It hasn’t worked and I’m not sure how it can work,” Vickery recently said.
“I’m also convinced that he couldn’t say no. How can you say no when Barcelona come knocking? As a Brazilian, you could never say no, but there are clearly two problems.
“One is that they signed him as an [Andres] Iniesta replacement, and he’s not. Nobody’s an Iniesta replacement, but certainly not Coutinho.
“He’s not a genuine midfielder, he does his best work in the final 30 metres of the field. He was signed for a role that he’s not fit for.
“Also with [Luis] Suarez losing a little bit of pace, that’s why [Ousmane] Dembele is ahead in the pecking order.
“You can’t see him fitting into the midfield three and you can’t see him fitting into the front three – and his relationship with the supporters seems to have broken down.
“The problem is Barcelona spent so much money on him; how much of a loss are they prepared to take to offload him?
“The most logical place for him to come, surely, would be the Premier League. He did very well at Liverpool.”
