Fellaini was also linked with a move to AC Milan and Inter showed last December however Mourinho chose to keep him at the club.
Fellaini headed Man United into a first-half lead, before Lukaku and McTominay came off the bench to register during a comfortable 90 minutes for the 20-time English champions.
Fellaini, 29, joined United from Everton in a £27.5m deal in 2013.
Manchester United eased to a serene 3-0 victory over Valerenga as the European leg of Tour 2017, presented in Aon, began in Norway.
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One of United's most impressive pre-season performers, Scott McTominay netted his first senior goal against Valerenga.
The deal is set to be announced in the next 24 hours and the Serbian could make his debut against Real Madrid in the Super Cup on August 8.
He could have scored again as well as he saw a shot blocked with the 'keeper out of his goal and then had another effort charged down late in the game after starting an attack with a good ball out to the wing.
Galatasaray sporting director, Cenk Ergun confirmed the club's interest in signing Fellaini, and it is suggested that all that remains is the agreement of a transfer fee as personal terms have already been agreed.
United deserved the advantage as they were clearly the better team, but their lack of width was telling as they often went too narrow rather than expanding the play. We want to try to avoid a Mourinho season. However, with Mourinho targeting a new midfielder, his game time could be limited even more and with the world cup round the corner, the Belgian will surely target proper game time to cement his position in the national side. "Marouane forget it. He's very important for me".