According to reports in Spain, both Arsene Wenger and Brenden Rodgers are keen to sign the 27 year-old defender.
Both managers will want to strengthen their defences as they push for the title next season and according to Spainsh reports, Fazio is the hottest target of both clubs.
Fazio has been impressive for Sevilla and was instrumental in their Europa League campaign last season which saw them lift the trophy.
Sevilla however are keen to hold onto their first choice centre back and will only let him leave if a club can offer £8m.
The Europa League champions have offered Fazio a lucrative new deal to keep him at the club but the defender is yet to commit his future to the La Liga side.
Fazio has also attracted attention from giants Barcelona, and according to reports Barca boss Luis Enrique sees the Argentine as an immediate replacement for veteran Carles Puyol who left the Camp Nou at the end of last season.
By Phil Wellbrook