Assou-Ekotto has been told he can leave White Hart Lane this summer, but the Lillywhites have as yet failed to find a buyer for the 29-year-old Cameroon international.
Following a successful temporary spell at Sunderland last season, Danny Rose has been first choice on the left side of Tottenham's defence for their two opening Premier League victories.
Although he is willing to offload Assou-Ekotto, Spurs manager Andre Villas-Boas is keen on recruiting some competition for Rose, but has apparently given up on his pursuit of Real Madrid star Fabio Coentrao.
According to the Daily Mail, Tottenham and Roma are discussing a deal that would see Balzaretti, 31, move to London on a season-long loan and Assou-Ekotto go in the opposite direction.
Balzaretti made 28 appearances for Roma last campaign after joining them from Serie A rivals Palermo.