The midfielder is apparently picking up 30,000 euros a season, but will see his earnings increase to 500,000 euros a season if he extends his contract to 2016.
Florenzi, 21, has scored twice in the opening three games of the season since returning to Roma from a loan spell at Crotone. His contract expires next summer.
Roma are seventh in the Serie A standings with four points from three games, but suffered a setback on Sunday when they squandered a two-goal lead in losing 3-2 at home to Bologna.
Florenzi scored the opening goal but it was to prove fruitless.