Arsene Wenger remains in the market for a top class goalkeeper according to the story.
The Uruguayan featured in Arsenal's comfortable 4-1 win over the Turkish champions in October this season, before sitting out the return leg in Turkey, which the Gunners also won 4-1.
The report states that Galatasaray are holding out for a fee of £15 million for their number one, with Arsenal considering the Uruguayan as an alternative to Chelsea's Petr Cech.
Muslera's appearance at the Emirates was notable because it saw David Ospina make his debut for the club, coming on after Wojciech Szczesny was dismissed on the hour.
The 28-year-old has made 160 appearances since switching to Istanbul from Lazio in 2011, also scoring a penalty for his new side in his first season. Muslera has also impressed during his time as Uruguay's first choice 'keeper, and currently has 66 caps to his name as he prepares for his country's Copa America defence.
Arsenal's goalkeeping situation remains uncertain, with both Wojciech Szczesny and David Ospina sharing duties between the sticks the season yet failing to absolutely convince their manager.