The Palermo player has travelled to London ahead of a transfer, according to Sky Italia’s Gianluca Di Marzio.
The deal would be a paid loan with an option to buy at the end of the season.
The 27-year-old has played six games for the senior national team since 2010. He will be expected to provide competition to Arsenal’s first-choice goalkeeper Wojciech Szczesny, who has endured an uncertain start to the season.
Viviano joined Palermo from Internazionale in 2012, but was quickly loaned to Fiorentina, where he spent last season.
The keeper is a lifelong Fiorentina supporter and has a tattoo of the club symbol, while he named his daughter Viola after the club's nickname.
Viviano, who was heartbroken when the Tuscans chose not to make his loan permanent, has been linked with several other clubs this summer, including Milan, Torino, Roma and Napoli.
Palermo are whittling down their squad after relegation to Serie B. Werder Bremen have just signed defender Santiago Garcia on loan, with an option to buy at the end of the season.