The report claims that the Gunners wish to complete a deal for the talented fullback this month, rather than risk losing out on him in the summer amid heavy competition for his signature.
The 19-year-old has come through the Leicester youth ranks and impressed upon breaking in to the first-team squad, attracting the interests of a number of high-profile clubs.
The Mirror report that he was the subject of a failed £3 million Arsenal bid last summer, while rivals Liverpool and Manchester City are also keen on bringing him in.
Chilwell is predominantly a left-back but he is also capable of playing on the opposite flank, potentially giving Arsenal plenty of options.
With Nacho Monreal 29, and Mathieu Debuchy in his thirties, both players are entering the twilight years of their respective careers and Arsene Wenger may see Chilwell as a long-term replacement option.
Leicester have been unable to tie the England U21 international down to a long-term deal and they may prefer a sale now rather than risk losing him for free further down the line.
Chilwell has made three appearances for Leicester this season, all coming in cup competitions.