The England international is likely to slot straight into central defence, joining fellow new arrival Aaron Wan-Bissaka in the rearguard.
Speaking about Maguire in his pre-match press conference, Solskjaer said: "Harry is ready to play. I am sure he will put himself up, when I ask him on Sunday morning, if he is available, because he has played many games for Leicester over the pre-season. He has trained well and he has looked sharp."
David de Gea is close to signing a new contract at Old Trafford and will start in goal while Victor Lindelof and Luke Shaw will complete the back four and Scott McTominay could get the nod in central midfield after impressing in pre-season.
There were doubts over Paul Pogba’s fitness after the Frenchman suffered a back spasm in training which ruled him out of the friendly meeting with AC Milan, but Solskjaer has revealed the World Cup winner is fit to face Chelsea.
“Paul joined in, actually, the day after [the AC Milan match]," revealed Solskjaer.
"I wasn’t going to risk him, travelling down with the flight, but he joined in the game against Blackburn the day after, behind closed doors here. He is available. All of the boys are fit.
Man Utd team news: Paul Pogba is minor fitness doubt to face Chelsea (Image: GETTY•buildlineup.com)
"It was always our aim to get to the starting line with as many players as fit as possible. Of course, Eric’s injury is bad news but the rest of them are available.”
Nemanja Matic and Fred were set to step in if Pogba was unavailable while Jesse Lingard and Juan Mata will compete for the No 10 role.
Alexis Sanchez is still short of match fitness, having missed the majority of pre-season because of international duty, but Solskjaer spoke positively about the Chilean in his press conference.
“Alexis has come in and trained well. Of course, he's four or five weeks behind the boys and he's not played apart from a one behind-closed-doors [friendly] here, so I think he'll see this as an opportunity, as well, to make his mark,” said the United boss.
Man Utd team news: Harry Maguire joined from Leicester for £80m (Image: GETTY)
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Daniel James also looks set for a competitive debut on the right wing while Anthony Martial has shone over the summer and should line up on the opposite flank.
Marcus Rashford will lead the line, although Solskjaer may choose to rotate the 21-year-old with Martial throughout the match – having played both as lone strikers in pre-season.
Eric Bailly is sidelined for up to five months after suffering a meniscus injury in the summer while Timothy Fosu-Mensah also underwent knee surgery and is unavailable.