Leicester have made Graham Potter their top target to replace Cooper, although the Independent report there are obstacles to overcome which may see them turn to their shortlist of alternatives.
Potter, 49, has been out of work since leaving Chelsea in March 2023 and despite being linked with several Premier League vacancies, he is yet to take up a new role.
The report claims his wage demands could prove to be a stumbling block, while the Englishman may have his sights set on joining a bigger club.
He was Leicester’s first choice in the summer to replace Enzo Maresca, who left to take charge at Stamford Bridge, before they eventually turned to Cooper.
If Potter decides to reject them again, the door would be open to Van Nistelrooy returning to the dugout in the Premier League after bidding farewell to United earlier in November.
Leicester are considering other names as part of their interview process and the 48-year-old impressed in his four-game stint as temporary boss at Old Trafford.
United remained unbeaten for that short period of time after sacking Erik ten Hag, with Van Nistelrooy managing to steady the ship by securing three wins and a draw to round off his reign.
Two of those victories ironically came against Leicester – a 5-2 thrashing in the Carabao Cup and a 3-0 success in the league on November 10 – before Ruben Amorim arrived and Van Nistelrooy subsequently departed.
The Dutchman also has experience from his time working in the Netherlands with PSV Eindhoven, where he won the KNVB Cup in 2022-23 and finished his reign with a 64 per cent win percentage.
United icon and his former team-mate Paul Scholes predicted it would only be a matter of time before Van Nistelrooy gets the itch to become a head coach again.
“When you see him on the sidelines, there’s that passion there. He even dresses like a manager. He looks like a manager,” Scholes said on TNT Sports after United beat PAOK in the Europa League.
“I’m pretty sure he must have the bug back to be a manager. Going back to being an assistant, it must be quite difficult because you’ll be frustrated. I think he should be a manager.”