According to the publication, the 26-year-old will cost in the region of £5million, after recently intimating his desire for a new challenge abroad, and that he will not be extending his deal beyond 2014.
Gunners boss Arsene Wenger has been credited with an interest in bringing the Argentine to the Emirates Stadium, as he looks to strengthen his defensive line ahead of the 2013/14 campaign.
Fazio's ability to operate in a more advanced defensive midfield role is also an attractive attribute for the Arsenal manager, as he still seeks a long-term replacement for Alex Song, who swapped north London for Barcelona last summer.
Having made 24 La Liga appearances for Sevilla this season, the South American stopper has proven to be an astute signing, since arriving at the Ramon Sanchez Pizjuan in 2007.
Arsenal fans will just hope that if Fazio does come north London he will be more successful in the Premier League than fellow Andalusian Sebastien Squillaci, who has struggled to ever really establish himself in Wenger's first-team.