The 27-year-old is surplus to requirements at Stamford Bridge, with new manager Frank Lampard set to favour academy graduate Reece James as deputy for Cesar Azpilicueta at right-back.
Goal can confirm that Roma have made an enquiry as to the availability of Zappacosta, but it is understood that paying such a price is beyond their means.
They could still explore a loan-to-buy deal in a bid to lower the costs due this summer in a bid to get their man.
Paulo Fonseca is reshaping the squad at Stadio Olimpico following a disappointing sixth-place finish under Eusebio Di Francesco and Claudio Ranieri last term.
It is understood that despite their interest in Zappacosta, the Giallorossi's priority at present is signing a defensive midfielder ahead of the September 2 deadline, with Steven Nzonzi currently in talks with Galatasaray regarding a move to Turkey.
They are also in the market for a centre-back, though a move for Dejan Lovren has broken down after Liverpool grew frustrated with Roma's negotiating tactics.
Chelsea, meanwhile, are keen to offload a number of their squad players in the coming weeks as they take advantage of the continental window staying open longer for European clubs than the Premier League's.
Zappacosta is joined on the chopping block by midfielder Tiemoue Bakayoko, who is way down the pecking order after failing to impress Lampard in pre-season.
Paris Saint-Germain have previously shown an interest in taking the France international back to his homeland while Galatasaray have held talks regarding a potential deal.
Lucas Piazon, meanwhile, is being offered around to various clubs as Chelsea look to loan him out for the seventh successive season.
Kenedy and Michy Batshuayi, however, look set to remain with the club having impressed Lampard during pre-season.
Kenedy, meanwhile, has spent the past 18 months on loan Newcastle but was one of the Blues' standout performers ahead of the new campaign.
Neither has made an appearance in Lampard's opening two competitive games in charge but have been assured of minutes in the weeks to come.