Reports in Italy indicate Roma want to sell the youngster, who has most recently been on loan with Serie B side Latina.
The Whites missed on on his signature back in January, after Massimo Cellino revealed a potential deal had collapsed because of the player’s extortionate wage demands.
Sources in Italy suggest a move could be back on, but Leeds could face stiff competition from Lazio, Palermo and Werder Bremen, most of whom could afford to pay the players high wage bill.
If reports are true, this could be the third time Leeds have shown interest in the midfielder, who has represented Italy at U21 level on 10 occasions.
Leeds owner Massimo Cellino appears to be a big fan of Viviani’s, who attended pre-season games with the Leeds owner before the start of last season, but then opting for a loan move to Latina.
Cellino could also take a front seat in transfer dealings this summer, after criticising new manager Uwe Rosler after his transfer activity at former club Wigan Athletic.