Bassini bought the Hornets 15 months ago when he fronted Watford FC Limited's £440,000 takeover.
BBC Three Counties Radio commentator Jon Marks said: "I think there could be quite a swift conclusion.
"The timing is crucial as planning needs to start. If it happens it needs to happen sooner rather than later."
Giampaolo Pozzo has owned Serie A side Udinese since 1986 and bought Spanish La Liga outfit Granada three years ago, but his son Gino is expected to be in charge at Vicarage Road should the takeover be completed.
Regarding the potential sale, Bassini told the Watford Observer: "I can't confirm that I will definitely leave because I do not know if they have the money for definite.
"If they do then it could be in the next 48 hours.
"I have been here 14 months and I do not see my daughter at the weekends. I like to do everything with her and she doesn't like football so that is a massive reason [in deciding to sell]."