The 27-year-old has yet to receive a concrete offer from another club although interest is expected to heat up once the Premier League transfer window closes on August 8.
This could propel Italy international Zappacosta into talks with clubs in his home country, which would be his preferred destination after a two-year stint in England.
Chelsea are unconcerned about delays over resolving Zappacosta's future as they have decided on Reece James as their alternative right-back.
James is expected back in training in the next two to three weeks following an ankle ligament injury and new manager Frank Lampard is keen to keep the pathway open for the 19-year-old after an impressive loan spell at Wigan Athletic last season.
Chelsea will only be allowed to register 17 foreign players for the Champions League this season and have been in talks to reduce the number by selling several stars.
Kurt Zouma and Michy Batshuayi are set to stay after coming back from loan spells from Everton and Crystal Palace respectively. This leaves Chelsea needing to offload either Zappacosta, Kenedy or Tiemoue Bakayoko, who have all featured heavily under Lampard in pre-season.
Zappacosta has made 52 appearances for Chelsea since joining two years ago in a £23m ($28m) move from Torino, but he has only started in 65 per cent of those games.
He has consistently been used as a back-up for either Victor Moses or Cesar Azpilicueta under both Antonio Conte and Maurizio Sarri in his time in west London.
Zappacosta joined Chelsea in the summer of 2017 when the Blues also signed Alvaro Morata, Danny Drinkwater, Bakayoko and Antonio Rudiger.
With Morata having already agreed on a permanent exit to Atletico Madrid at the end of the 2019-20 season, Rudiger could be the only Blues player left from that £186m ($226m) spending spree.