Viviani, who has 10 Italy Under 21 caps to his name, has been heavily linked to the West Yorkshire club amid an influx of summer arrivals from Italian football.
The 22-year-old had loan spells in Serie B with Pescara and Latina during the last campaign and is expected to depart the Stadio Olimpico after making just nine first-team appearances in all competitions since his 2011 debut.
However, agent Giovanni Ferro confirmed that Leeds would face competition from a number of top-flight Italian sides for his signature.
"We are speaking with Leeds United but the player has a lot of interest from Italian Serie A clubs," he told the Yorkshire Evening Post.
"We’ll take a decision in the near future."
Goalkeeper Marco Silvestri, midfielder Tommaso Bianchi and striker Souleymane Doukara have already completed moves to Elland Road from Italian clubs, with further additions expected in time for the start of the new Championship season.
Former Arsenal stopper Stuart Taylor has also penned a deal with the Whites, while controversial former Newcastle forward Nile Ranger is understood to have been offered the chance to go on trial this summer.
Meanwhile, Sampdoria full-back Gaetano Berardi is reported to be nearing a switch as president Massimo Cellino continues his rebuilding of the club.
David Hockaday’s men have just returned from a two-week pre-season training camp in northern Italy and are set to play their first friendly on home soil away to local side Guiseley on June 19.