The Italians are understood to be offering far less than Gallas's current £80,000 a week deal, even though the France defender would be available on a free transfer at the end of the season.
Roma's sporting director Daniele Prade has been in London this week, though Gallas was not his only focus.
Rout: Emmanuel Eboue scores Arsenal's fourth against Porto this week
As well as watching four Porto players during their Champions League defeat by Arsenal on Tuesday night, he is also keen on versatile Gunner Eboue.
However, with the cash-strapped Italians looking for bargains, a deal for the Ivory Coast international is likely to be difficult to pull off.
Eboue was close to an exit last summer, particularly after the Emirates crowd turned against him, but he has gone on to be a consistent and regular performer this season.
His versatility has also attracted other clubs in Italy and European champions Barcelona.
Running down: William Gallas (right) is out of contract in the summer
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