Solskjaer laughed off suggestions Greenwood is being punished for breaching club rules and insisted the striker is injured despite taking part in a training session at Carrington on Monday morning.
"Where are your sources, that's what I'm saying," Solskjaer said in a news conference on Monday when asked if Greenwood has been sanctioned.
"I can't declare medical stuff can I? We hope it's just a niggle and we don't want to take any chances with him and hopefully at the weekend it'll be fine again."
"We hope Harry will be fit for the weekend, we're not sure but we hope so," said Solskjaer. "We've lost a couple. Bailly didn't travel or Lingard didn't travel, we're a little bit depleted but have more than enough players."
Solskjaer revealed that in Maguire's absence, Bruno Fernandes will captain the team for the first time despite only arriving in January.
The news came as a surprise to the midfielder, who was sat alongside Solskjaer at his news conference.
"I was not expecting this," said Fernandes. "For me it's an honour.
"To be captain of Manchester United is an important achievement for me, but I think everyone is the captain, everyone needs to help and be a leader in their own way."