The Gunners had bid of £3.5 million rejected for the 19 year old back in the summer and Wenger is ready to return with an improved offer this month.
Chilwell has attracted a lot of interest from several Premier League clubs following and impressed for the Foxes during his first team appearance against Tottenham earlier this month. The young English defender is expected to replace Kieran Gibbs at Arsenal.
Gibbs is angling for a move away from Arsenal due to the lack of first team action and could be sold in the summer.