The coronavirus crisis is set to have a major impact on the summer market, with reduced budgets likely to lead to lower fees and wage packages.
Old Trafford bigwig Woodward previously admitted spending big on players would ignore the reality of the financial situation facing football clubs.
Gary Neville, however, has insisted that a number of top-quality additions are required if the Red Devils are to challenge the top two.
Solskjaer agrees with his former team-mate’s assessment and said: “Gary is right in a lot of things he says and of course we cannot think we’re there.
LATEST LIVE SPORT TV DEALS
Get Sky Sports for just £25 per month for 3 months
Get BT Sport for HALF PRICE
“If you look at the table, we’re nowhere near where we should be. Consistency has to be improved and we still have to improve on many aspects of the game.
“I don’t know how many points we’re behind the top two, but Gary’s right – there’s definitely not going to be any complacency and thinking, ‘We’ve cracked it’ because we’ve got so much to do.
“It’s an enjoyable journey. We can see improvements but, yes, we need to make one or two – or more – very good decisions. It’s going to be an important summer, definitely.”
While Solskjaer admitted “one or two” new arrivals would help, the Evening Standard claim he is looking to make at least three major signings.
Transfer news LIVE: Sancho Man Utd agreement, Havertz to Chelsea, Arsenal contract twist
Borussia Dortmund winger Jadon Sancho remains his top target, although a fee could prove difficult to agree due to United’s reluctance to spend in excess of £70million on one player.
Aston Villa captain Jack Grealish and Ajax midfielder Donny van de Beek are also on Solskjaer’s wanted list.
And the Norwegian revealed he is placing an emphasis on signing players with “a certain DNA and identity”.
“I’m very old school in my values. I’m not going to rant and rave. I’d rather open the door or close the door. Either in or out,” he said.
“Players who want to sign if they don’t feel right as a person you close the door, players who are inside who don’t feel right and don’t want to contribute to the team ethos and have the betterment of the team at heart then you open the door and let them leave.
“It’s a constant process. Whatever you do every day, that will decide if you’re going to be part of Man United or not. I hope and believe I will always stay true to my principles and values of that.”
The United boss added: “It’s going to be a strange transfer window and I don’t expect a lot of big transfers maybe. I don’t know.
“We don’t really know how the market is going to be. For us as a team, club and staff, we need to work really well. It’s about the consistency.
“I’m not just talking about decisions off the field – it’s also here in and around the training ground.”
United can climb to fourth place – for the time being – if they beat Bournemouth in this afternoon’s Premier League clash (3pm).
This article contains affiliate links, which means we may receive a commission on any sales of products or services we write about. This article was written completely independently, see more details here