According to Goal, the Reds will step up their attempts to bring the Foxes wide man to Anfield over the coming week after being linked to the club for many months.
However, the website report that there could yet be a hold up in the potential move, with the two clubs yet to agree on a fee.
Liverpool are understood to be willing to pay up to a certain amount for the defender, and are unwilling to break the bank as they are aware that the teenager is in the last year of his contract.
However, Leicester are not keen to lose one of their prized assets, and the Reds are expecting the Premier League’s unlikely champions will expect a hefty fee for a talented youngster who they expect will advance to the England senior side one day.
Chilwell is a left-back, who is celebrated for his excellent touch, his passing ability and his maturity in possession.
The youngster could provide competition for Alberto Moreno, whose reputation has taken a severe beating following his dismal showing in the Europa League final.