The 32-year-old, who was part of the Foxes side which cruised to the Premier League title in 2015-16, has made just five appearances in the top flight this term (Transfermarkt), and his contract expires at the end of the season.
According to the Daily Mail, Simpson is one of two players who have been earmarked as prime candidates for a departure from the King Power Stadium this summer, along with Shinji Okazaki.
The report states that the right-back, who has lost his place in the starting XI to 2018 arrival Ricardo Pereira, is yet to engage in talks with the Leicester hierarchy over a new deal, so it looks increasingly likely that he could become a free agent.
Although the Mail does not completely rule out the possibility of the Foxes offering Simpson a new contract, it believes that new manager Brendan Rodgers is expected to first see whether signing a new right-back to challenge Pereira makes more sense.
Valued by Transfermarkt at £3.6million and with a Premier League title win on his CV, the possibility of snapping Simpson up on a free is something that the Magpies should consider, especially given they were linked to him back in January, as was reported by the Mail.