The 36-year-old midfielder, who left AC Milan on a free transfer last month, was expected to tie up a deal with the Viola last week.
"There is no news over the last few days, so we'll have to wait and see what happens next week," Moreno Roggi told Radio Blu.
"The player already expressed his preference for Fiorentina, now the club must decide whether there's space for him in the squad.
"We're waiting to know if Fiorentina think Ambrosini would be of use to them or not."
West Ham United have also been linked with the experienced midfielder.