The Sunday edition of Sport via Sport Witness suggests that both Leicester and Premier League rivals Watford have enquired about the availability of the 24-year-old, who is supposedly being forced out of the Catalan club as he does not feature in manager Ernesto Valverde's plans.
Alcacer himself has now supposedly accepted that his future lies elsewhere after initially being reluctant to leave the club this summer and is reportedly 'studying' offers from England.
However, the report also suggests that Watford have been entirely ruled out of contention, with the Spain international more keen on a move to Leicester.
Southampton had previously been linked with a move for Alcacer but are not mentioned at all in the Sport article, suggesting that the Foxes have now seized the initiative in the race for the striker's signature.
With the likes of Jamie Vardy, Kelechi Iheanacho and Islam Slimani already at the club, Leicester's need to sign Alcacer is not instantly clear. However, it is possible that the club could look to offload a striker or two this summer, with Iheanacho struggling in his first season at the King Power Stadium and Slimani spending the second half of 2017/18 on loan at Newcastle.
Alcacer joined Barcelona from Valencia in 2016 for €30m but has struggled to make any kind of meaningful impact at the Nou Camp, making just 37 appearances in La Liga during that time.
However, a return of 15 goals in 50 appearances suggests that Alcacer has goals in him and could certainly make an impact if utilised properly at another club.