The France defender is out of contract in the summer and the Gunners' policy of only offering one-year deals to players over 30 could tempt Gallas to look elsewhere.
Arsene Wenger is keen to hold on to his compatriot and may bend the rules by offering a two-year deal, but cash-strapped Roma are ready to pounce.
Stalwart: Gallas (right) has been a regular in the Arsenal defence
Old friends: Gallas with Ranieri and Hernan Crespo (right) during his time at Chelsea in 2004
The Italians are already free to negotiate with the 32-year-old because he is in the final six months of his current deal.
Roma boss Claudio Ranieri brought Gallas to England when in charge of Chelsea in 2001 and is keen to work again with the former Marseille centre half.
Wenger is reluctant to lose one of his most experienced and reliable performers. Gallas may have been stripped of the captaincy 16 months ago, but he remains a rock at the heart of Arsenal's defence and has missed just two Barclays Premier League games all season.
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