The Netherlands international is in line to return to the squad for the Europa League tie with AC Milan on Thursday after recovering from injury.
He has made just two Premier League starts following his £40 million move from Ajax in the summer but Solskjaer has branded reports the 23-year-old wants to leave Old Trafford as "speculation".
"There is always speculation here," Solskjaer told a news conference on Wednesday. "Donny has been focusing really hard and working really hard to get back available for the latter stages of the season so that's our focus."
Van de Beek has been linked with a return to Ajax but on Wednesday, Netherlands legend Ronald de Boer dismissed the stories after speaking with the Dutch side and Van de Beek's agent.
"I spoke to Ajax and they said there's no truth in it at all," De Boer told talkSPORT.
"He didn't ask to speak to them. He's just focusing on his recovery on his ankle, and it's not true that he asked Man United to leave."
Speaking ahead of the trip to Milan, Solskjaer also insisted defender Diogo Dalot has a future at the club despite spending this season on loan at the San Siro.
Dalot was part of the Milan team which earned a 1-1 draw at Old Trafford and is set to keep his place for the return leg on Thursday.
"The main thing for Diogo [Dalot] was to be fit, he never managed to be fit for a long spell when he was here because of injuries and now he's kept fit all season and been available for them he's playing at a big club," Solskjaer said.
"It's been a good year for him so of course I've been very pleased with his development this season. He's our player and I'm looking forward to having him back."