The 29-year-old spent the second half of last season on loan at Spanish side Sevilla, who have a £5m option to buy clause as part of that deal.
Layun can operate as a full back on either flank, as well as in a defensive midfield role, offering great versatility to whatever side that does sign the Mexico international.
After struggling for minutes in Portugal early in the season, Layun made 16 La Liga appearances and scored two goals following his January loan switch to Seville.
Layun is part of Mexico's World Cup squad in Russia this summer, and played during his country's remarkable victory over Germany.
The 29-year-old struggled to find his shooting boots in that match, but still emerged as one of his nation's top performers in a tournament they're already beginning to impress in.
Layun has 64 senior international caps to his name, scoring six times for El Tri.
Layun already has experience of English football, joining Watford in January 2015. He played 20 league games for the Hornets during his spell with them in 2015, featuring in both the Championship and Premier League.
He scored his only league goal for Watford on his Premier League debut - in a 2-2 draw in August 2015, against Everton at Goodison Park.
Layun isn't the only player Arsenal are reportedly keeping tabs on during this World Cup, with the London club reportedly scouting Russia's creative midfielder Aleksandr Golovin.
The 22-year-old, who plays his club football for CSKA Moscow, has attracted significant interest this summer.
Arsenal boss Emery is understood, according to Sport Express, to have sent scouts to the tournament to report on the player.