The 21-year-old has emerged as one of the most promising young defenders in the English Football League since Paul Lambert took charge at Portman Road, making more than 20 appearances after being loaned to Swindon last term.
Although it remains unclear if United would consider signing Woolfenden now - or are tracking his progress before deciding to make an approach at a later date - he fulfils nearly all of the criteria they look for in potential new recruits.
Crucially, despite usually being deployed in a central role, Woolfenden can also operate as a full-back; meaning he appears well-suited to the challenges of United’s 3-5-2 system, where manager Chris Wilder feels they lack cover for Jack O’Connell and Chris Basham.
Elias Cobbaut, a Belgium under-21 international currently with RSC Anderlecht, is also known to interest Wilder although, given his recruitment budget, the former KV Mechelen protege could prove difficult to extract from Lotto Park.
The 34-time Belgian title-winners paid Mechelen £2.5m to sign Cobbaut, aged 22, two years ago and are thought to want a near five-fold return on that investment in order to part company with one of their most exciting prospects.
Adrien Tameze of Nice is another name linked with a move to Bramall Lane in recent weeks.
With his side well-placed to secure an immediate return to the Championship after being relegated last season, Lambert is reluctant to sell any members of his first team squad.
But the financial constraints associated with third tier football mean at least one could be offloaded before the forthcoming deadline. And that might pave the way for Woolfenden to be offloaded, given his growing army of admirers.
United, who unveiled former England midfielder Jack Rodwell earlier this month, travel to Arsenal in the Premier League on Saturday.