Ba joined Chelsea from Newcastle last January but has failed to cement a regular first-team place under either Rafa Benitez or Jose Mourinho.
Representatives of the Senegal international have been in touch with the Serie A club, which made an inquiry for the 28-year-old in the summer.
The Blues want 15 million euros for Ba, just less than double what the club paid for him almost a year ago, but Roma is unlikely to be interested at that price.
Arsenal, meanwhile, maintains an interest in Ba but as was the case in the summer, when Mourinho blocked his potential move to the Emirates and instead sent Romelu Lukaku on loan to Everton, Chelsea is unwilling to sell to a direct rival for the Premier League title.
Ba has scored three times in 12 appearances this season, including the winner in Wednesday’s Champions League victory over Steaua Bucharest, but has started only two Premier League games.
Roma began the season with a record 10 consecutive victories but has drawn four of its last five matches and has slipped to second in the Seria A standings, three points behind league leader Juventus.