The 18-year-old is currently out on loan with Championship side Huddersfield Town. While he has only made two appearances for David Wagner's side, The Telegraph report that Chilwell is one of the brightest prospects in the game, having captained England's U20 side.
Chief scouts from both of the Premier League giants were in attendance for the Terriers' most recent game against Birmingham City (via Telegraph). And they would have undoubtedly been impressed by what they saw. Chilwell helped to keep the play-offs contenders at bay, as Huddersfield came away with an excellent 2-0 victory.
The Gunners may be considered as favourites for his signature. The Telegraph report that they have previously made a bid for the left-back, and are keen to tempt Leicester with another offer.
But while Huddersfield will have no say in his next destination, Wagner's relationship with Reds manager Jurgen Klopp - having worked with Klopp at Borussia Dortmund - may strengthen the Reds' desire to sign the prospect, and may result in his current manager trying to convince the youngster that Liverpool is the best place for him.
However, staying at Leicester cannot be ruled out as a potential option. The Telegraph report that the Premier League leaders plan to offer Chilwell a new deal in the coming months, and hope to give him more first-team opportunities upon his return from his loan.