United have already been busy in the market, landing Daniel James from Swansea and Crystal Palace’s Aaron Wan-Bissaka.
Both men were brought in early in the window, allowing Solskjaer time to ease them into life at Old Trafford before the club’s tour of Australia.
According to the National, both signings were Solskjaer’s choice – and Woodward gave the green light for both deals.
United’s executive vice-chairman has been responsible for the club’s dealings in recent years due to the lack of a sporting director at the Red Devils.
Woodward has overseen some poor transfers during his time on the board, which has led to sections of the United fanbase blaming him for the club’s failings in recent seasons.
The likes of Radamel Falcao, Angel Di Maria and Memphis Depay are just some of the stars who failed to deliver at Old Trafford after signing for a significant fee.
Woodward and United are keen to strengthen even further this summer.
Solskjaer is understood to be keen on both Bruno Fernandes and Harry Maguire.
However, United are yet to reach an agreement with either Sporting Lisbon or Leicester for the respective stars.
The Foxes are demanding a whopping £90m for Maguire, who United think is valued at £75m.
And it’s clear Solskjaer doesn’t want to pay over the odds for new arrivals.
“We’re still in the market looking to do some business, but we’re patient,” he said in Perth this week.
“We’re Manchester United. We don’t have to sell and don’t have to overpay.
“You have to have the right players at the right price.”
For this reason, United are said to have been priced out of a move for Newcastle youngster Sean Longstaff.
The Magpies want £50m for the midfielder who has only made a handful of appearances in the first team.