The Foxes are still yet to make a first-team addition this summer, a consequence of a lack of transfer funds and failing to receive offers for some of their players.
However, earlier this week, it was claimed that Nice were closing in on the signing of long-serving goalkeeper Kasper Schmeichel.
Should the Dane move to the South of France, Brendan Rodgers would be able to promote Danny Ward up the pecking order to replace the veteran.
Nevertheless, according to Get French Football News, it appears that the Northern Irishman is contemplating whether to make an approach for Leno.
Since moving to the Emirates Stadium in June 2018, Leno has made 125 appearances in all competitions, the German being regarded as first choice for a number of seasons.
However, the 30-year-old fell behind Aaron Ramsdale during 2021-22, being restricted to just four outings in the Premier League.
With Matt Turner having already arrived this summer, head coach Mikel Arteta is prepared to part ways with Leno as soon as possible.
Newly-promoted Fulham have been heavily linked with the former Bayer Leverkusen stopper for a number of weeks, but there has been a reluctance to meet Arsenal's alleged £10m valuation.
According to the Evening Standard, the two teams are now ready to reach a compromise of £8m, keeping the Cottagers as frontrunners for Leno's signature.
Leno could be left with a choice of continuing his career in England's capital or taking the opportunity to move to the East Midlands.
The report adds that Leicester also hold an interest in Alban Lafont, who has starred for Nantes during the last three seasons.
However, the Ligue 1 outfit are allegedly open to cashing in on the former France Under-21 international, who has two years remaining on his contract.
Nantes are reportedly prepared to sell Lafont for a fee in the region of £17m.