According to the Telegraph, the 31-year-old right back has become a top target for Gary Rowett’s side to bring to the Bet365 Stadium on a one-year loan.
Despite the closing of the transfer market, Rowett is still looking to secure a loan deal for the defender, to help bolster his squad in the pursuit of promotion back to the Premier League.
Stoke City already have the likes of Moritz Bauer vying for the starting right full back spot, but Simpson would add competition for places if the deal can be secured.
Leicester City head coach Claude Puel looks set to allow Simpson to depart from the King Power Stadium this summer, as he has cover in the full back positions.
The defender, who has been on the books at the Foxes since 2014, has made over 120 appearances for the club, and played an integral part in the Premier League title winning side of 2016.
Simpson already has experience playing in the second tier of English football, having made Championship appearances for the likes of Sunderland, Ipswich Town, Newcastle United and Queens Park Rangers throughout his 12 year career to date.