Brighi, 27, has been with the Italian capital club since 2004 but he was sent out on loan to Chievo Verona for three seasons. He returned to Roma last term but he has been more of a fringe player in Luciano Spalletti's side.
Now, his agent Vanni Puzzolo has revealed Celtic's interest, while at the same time reiterating his frustration with Roma - who insist they want to hold on to the midfielder yet have been slow to make a new contract offer.
Puzzolo said to the Daily Express: "We must now discover what Roma's plans are for the player.
"Only after that can we think about Celtic.
"The club is guaranteed Champions League football and plenty of Italian players have gone to Scotland and enjoyed success.