The 18-year-old is considering his future at Old Trafford after a difficult season in which he has made just two Premier League appearances — including on the final day against Cardiff.
Paris Saint-Germain were credited with an interest in him on Tuesday in the Portuguese press.
Solskjaer also failed to name the Portuguese teenager when he was discussing young players who could be involved in the Europa League for them next season.
He recently said: ‘I’m an optimist by nature, so you will make the most of (the Europa League), is it giving players like Chongy, Mason Greenwood, James Garner game time? We have to make something positive out of it, no matter what.’
While he is expected to be involved over pre-season when United travel to Australia, Gomes is considering his future.
He is in a strong position too, with his contract with United set to expire next summer.
And that could lead to Barcelona making a move. European sides have stepped up their recruitment of England-based youngsters in recent years, such as Jadon Sancho’s switch to Borussia Dortmund from Manchester City.