The report also suggests that United will face competition for the Danish international from Chelsea, who are also in need of strengthening at the back.
Schmeichel would represent strong back-up for United’s Spanish international goalkeeper David de Gea, who has been in poor form for a couple of years but who suffered a serious downturn in his performances after the coronavirus pandemic lockdown.
Leicester have identified Sergio Rico of Sevilla - who spent the season on loan at Paris Saint-Germain - as a potential replacement after the 26-year-old stopper conceded he would not start ahead of their Costa Rican first choice, Keylor Navas.
United have Sergio Romero has a second choice in goal but the Argentine is not good enough to be considered a long-term replacement for De Gea. Schmeichel would be a good fit as he has yet to play for a major side and may be willing to sit on the sidelines while United engineer a way out for their highest-paid player.
Chelsea need a new goalkeeper after Frank Lampard lost faith in Kepa Arrizabalaga. The 25-year-old Basque is expected to be sold or moved on back to Spain with it looking impossible for him to win back his place.
With the amount of money that Chelsea have already spent in the transfer market and with Kai Havertz expected to arrive, and given United are focusing their efforts on the £100 millionish Jadon Sancho, neither of them can afford to spend big on a replacement goalkeeper.
Schmeichel has a contract that runs for the next three seasons so there is little chance that Leicester would sell on the cheap, but at 33 there may be a willingness to earn some cash from a sale.