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The BBC understands that the Foxes have made a pair of bids worth in the region of £20m ($25.7m) that fall short of Chambers' £28m valuation. It is also said that Arsenal have now changed their stance with regard to selling the former Middlesbrough loanee since they discussed a potential deal with Crystal Palace in July.
Chambers has made 59 senior appearances for the Gunners since arriving from Southampton in 2014, but moved to the Riverside Stadium last summer on a season-long loan.
He featured 26 times on Teeside after battling a recurring foot injury and later started all four of semi-finalists England's matches at the European Under-21 Championship in Poland.
After coming on as a substitute in an Emirates Cup tie against Benfica, Chambers, who is capable of playing at centre-back or on the right-hand side of defence, has yet to be included in an Arsenal matchday squad in 2017-18 despite Arsene Wenger's defensive options having been left significantly depleted at times.
Crisis-stricken Arsenal, who recently sold Alex Oxlade-Chamberlain to Liverpool in a deal valued at an initial £35m, have been eager to trim a bloated squad this summer and appear likely to sanction the respective departures of Jack Wilshere, Mathieu Debuchy and Lucas Perez having already offloaded Wojciech Szczesny, Gabriel Paulista, Kieran Gibbs, Carl Jenkinson and Yaya Sanogo.
Joel Campbell is reportedly heading to Real Betis, although The Mirror suggest that Shkodran Mustafi is set to stay put with Inter Milan's offer failing to match his valuation and Juventus having now loaned fellow German Benedikt Howedes from Schalke.
Leicester bought the impressive Harry Maguire from Hull City in July and are keen to further bolster their defensive ranks before Thursday night's 11pm BST deadline with their previously infallible centre-back partnership of Wes Morgan and Robert Huth having become susceptible to injury. Yohan Benalouane's future has also been subject to persistent uncertainty.
The 2015-16 Premier League champions have been unsuccessful with multiple offers for West Bromwich Albion captain Jonny Evans, who could be set to return to Manchester with Pep Guardiola's City. They are also believed to have submitted an enquiry for Liverpool exile Mamadou Sakho earlier this week.