The Hornets have already made an offer for Muslera, with his club Galatasaray understood to have already turned the bid down.
Muslera is currently under contract at Galatasaray until 2021. He played a key part in Galatasaray's title winning season last term, the fourth time in which Muslera has won the title with Galatasaray, and his 11th trophy overall. He also kept 13 clean sheets in 38 appearances last season.
He has made 99 appearances for Uruguay, and has kept two clean sheets in his nation's opening two games of this summer's World Cup. He was part of the Uruguay side who won the 2011 Copa America, and was also a member of the team who finished fourth at the World Cup in 2010.
Watford's current number one is Brazilian Heurelho Gomes, who made 26 appearances for the club last season. Orestis Karnezis, on loan from Udinese, played backup to Gomes, but as he has now returned to his parent club, meaning the club are keen to strengthen the position.
The 32-year-old left Italian side Lazio to join Galatasaray in 2011, and has gone on to make 281 appearances for the Turkish club. In that time, he has kept 89 clean sheets.