The 24-year-old Romanian has struggled to claim a regular role at White Hart Lane since joining from Steaua Bucharest last August and could be offered the chance to revive his career in Serie A.
Spurs are believed to be holding out for the £7.5m fee they paid for Chiriches, but Roma will attempt to negotiate a smaller asking price.
Chiriches, who made 24 appearances for Spurs, scoring just the one goal, has pulled out of the club’s pre-season tour of the United States and Canada due to a back problem.
He complained of stiffness in his lower back and remained in London for further treatment.
Midfielder Sandro missed the trip because of a virus and has also attracted speculation about his future, with reports suggesting he could join another Italian team Napoli or Russia’s Zenit St Petersburg.