The midfielder has agreed a season-long loan deal at Elland Road, with parent club Roma prepared to let him go in search of regular game time outside of the Italian capital.
No agreement for the 22-year-old has been pushed through, though, as the relevant paperwork is yet to be processed.
Leeds owner Massimo Cellino has claimed that he expects the deal to go ahead, despite pulling out of it at one stage, and he is hoping to hold further discussions on Monday.
There is, however, a chance that Viviani will have turned his attention elsewhere by then, with a return to Latina – a club he spent time on loan at last season – being seriously considered.
Viviani’s representative Giovanni Ferro told the Yorkshire Evening Post: "We think we can’t wait so much time to have the contract.
"Federico is really considering (playing) again for Latina."
While Leeds are continuing to pursue one midfield option, head coach David Hockaday has revealed that the addition of a new centre-half has also become a top priority in the wake of Tom Lees' departure to Sheffield Wednesday.
He said: "We've got two centre-backs, two senior centre-backs, so that's obviously somewhere we need to strengthen.
"We've got options and we're exploring them."