The report claims that the Dutch manager is on the lookout for a new shot-stopper following the exit of US number one Tim Howard with Manchester City’s Joe Hart another possibility.
Koeman looks all but set to trade Southampton for Everton after the two clubs agreed a compensation package (Sky Sports) allowing him to move to Merseyside.
The former Valencia manager will succeed Roberto Martinez and take over a talented but somewhat broken squad which needs a couple of major additions to lift morale around the place.
While a new centre-back, winger and striker would all be welcomed by the supporters, a new goalkeeper must be the top priority with current number one Joel Robles only deemed a decent back-up.
Schmeichel was instrumental during Leicester’s Premier League title victory, especially towards the end of the campaign when he helped his side keep a succession of clean sheets.
The Foxes have had to endure heavy interest in the likes of N’Golo Kante, Jamie Vardy and Riyad Mahrez, yet now Schmeichel has become the latest name linked with a move away.
The report goes onto say that Everton deem the Dane a realistic target, although the talented custodian is said to have no burning desire to leave Leicester and is currently in talks over a new deal at the club.