Manchester United chief Woodward is aiming to deliver for Solskjaer in the transfer market this summer.
The club are well aware investment is needed if they are to return to the summit of the English game, having gone six years without winning the Premier League title.
Manchester United finished sixth in the Premier League last term, in a nightmare campaign that saw them ship 54 Premier League goals, sack Jose Mourinho and lurch from one crisis to another.
Woodward vowed to back Solskjaer when speaking at a conference call last month, saying: “After a turbulent season, everyone at Manchester United is focussed on building towards the success that this great club expects and our fans deserve.
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“Preparations for the new season are underway and the underlying strength of our business will allow us to support the manager and his team as we look to the future.”
However, ESPN claim Woodward has already shelved interest in two Solskjaer targets this transfer window.
And that’s because he deems them too expensive.
The two players who have been in United’s sights are Jadon Sancho and Kalidou Koulibaly, of Borussia Dortmund and Napoli respectively.
Regarding Sancho, and many feel United have given up due to the fact they have no Champions League football to offer.
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Rivals Barcelona, PSG and Real Madrid all have that ace in their pack.
But it appears United are actually not pursuing a deal because they feel Sancho’s price tag to be too lofty.
Dortmund are demanding £80million to start negotiations for the former Manchester City winger.
And United also feel Koulibaly’s price tag of £90m is too big as well.
It means Solskjaer is now facing a trying first summer with the club signing just Daniel James so far.
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Speaking at James’ unveiling last week, Solskjaer expressed a belief that the forward has what it takes to be a United hit.
“Daniel is an exciting young winger with lots of skills, vision, exceptional pace and a good work ethic,” Solskjær said.
“He had a great season with Swansea and has all the attributes needed to become a Manchester United player.
“We are delighted and we are all looking forward to working with him.
“This is the perfect environment for Daniel to continue his development.”