Manchester United have made three signings this summer after confirming Harry Maguire as their latest addition at the start of the week.
The Red Devils have paid £80million to acquire Maguire from Leicester City in a deal that makes him the most expensive defender of all time.
That comes after the additions of Daniel James from Swansea City and Aaron Wan-Bissaka from Crystal Palace, spending nearly £70m to sign the duo.
But United have been left frustrated since then, with Paulo Dybala having rejected a move to Old Trafford after a swap deal with Juventus to send Romelu Lukaku had been proposed.
It has also been revealed that United do not have firm interest in signing Bruno Fernandes from Sporting Lisbon while a deal for Christian Eriksen of Tottenham has also collapsed.
United had looked into a cut-price deal for the Dane, who is out of contract in north London next summer, but he prefers a move to Spain to join Real Madrid.
But executive vice-chairman Woodward and manager Ole Gunnar Solskjaer have been told that their current squad, even despite bolstering their back-line with the signings of Maguire and Wan-Bissaka, is not enough to bridge the gap to the top four after finishing sixth last season.
Former Premier League goalkeeper Shaka Hislop told ESPN FC: “I still think that they need another centre-half. I think [Victor] Lindelof is good but not great, not the kind of centre-half United need if their ambitions are to be believed.”
Asked if they have the quality to match their quantity at the back, with United having six senior central defenders, Hislop added: “No they don’t.
“It’s a terrible term to use and I shouldn’t speak about modern day footballers in these terms as the least of the evils available to Ole Gunnar Solskjaer.
“But I don’t think anybody, [Chris] Smalling or [Phil] Jones, really fits the bill in terms of a top notch Premier League centre-back.”
United could sell Lukaku with the Belgian currently back in his homeland training with Anderlecht as he seeks an exit.
The striker has been linked with Inter Milan and Juve, with the former having a £54m bid rejected as United hold out for at least the £75m they paid Everton for him two years ago.
But Hislop has warned United they will be short offensively if they sell Lukaku without replacing him.
“[Mason] Greenwood’s, what, 17? I’m not sure. They don’t have out-and-out centre forward depth,” he declared.
“Without [Marcus] Rashford, I’m not sure who else you’d turn to as that out-and-out centre forward. I think [Marcus] Rashford is very effective on either wing. That gives you options in terms of how you play.
“But if Rashford goes down injured and Lukaku, something happens between now and the close of the transfer window, and you don’t have anybody else, you’re way too thin.
“Martial is an option but I’m really not convinced that he’s a good enough finisher to be playing through the middle. If Rashford goes down for a game or two and you have to use Martial in there, it’s one thing.
“But if you’re talking about your out-and-out centre forward being out for two months, having Martial or anyone else fill in for an eight or 10 game spell I don’t think works at all.”