Gomes has returned to training at Carrington since the coronavirus lockdown restrictions were lifted but, as things stand, will leave the club on June 30 when his deal expires.
The 19-year-old forward, who has made 10 senior appearances, including six this season, has been linked with a move to Chelsea, but Solskjaer believes he is set to stay.
"Angel is a top, top kid who we've had in the club for so many years," Solskjaer said at a news conference on Thursday.
"We've offered him a deal. Hopefully he'll take that, but if not, I'll wish him all the best. From what I understand, it's not too far away. If not, we'll wish him all the best."
After three months without a competitive game, United will restart their Premier League campaign with a trip to Tottenham on Friday night.
Rashford hasn't played since January because of a back injury, while Pogba hasn't featured since Boxing Day after undergoing ankle surgery.
United face four games in 12 days after the resumption, and Solskjaer said he will have to be cautious about the players' fitness.
"Of course, Marcus and Paul have been out for a long, long period," Solskjaer said. "They're available, but how long they're going to play for, let's see.
"We have to look after the players. They haven't played for a long period. The Premier League is intense, and they're going to go straight into a season afterwards as well. We have to look after them and take care of them."
Solskjaer also praised Rashford after the forward's campaign encouraged the UK government to extend a national voucher scheme to feed children from low-income families.
"It's an honour to have Marcus and what he's done during this lockdown," Solskjaer said. "He's been unbelievable -- [to] help so many people that need it. He's taken from his own experience when he was a kid. I know how much it means for the kids and we, as a club, are immensely proud of him.
"He's obviously a top footballer but also a fantastic human being -- a future leader, a future captain, maybe, of England, Man United, who knows? He's already captained the team [United]. We're really proud of him, and his family must be so proud as well of what he has achieved.
"As his manager as well, it's been fantastic to follow Marcus during the lockdown period; he got the prime minister to change his mind. Marcus is such a top human being -- he's changed the lives of so many kids this summer, which is more important than any game he'll play."
United were on a strong run of form before the pandemic halted Premier League football, with Solskjaer's men unbeaten in 11 matches and in fifth, three points behind Chelsea in the race for the final remaining Champions League qualifying spot.