The Blues bought Zappacosta on a four-year contract from Torino on deadline day in August 2017 when Antonio Conte was in charge.
The Italian was recruited as a back-up for Victor Moses in the 3-4-3 right wing-back position, and made 22 league appearances last season.
Conte left in the summer, however, and new boss Maurizio Sarri has reverted to a back four, selecting the experienced Cesar Azpilicueta as his first-choice right-back.
Zappacosta has thus played just 18 minutes – across two substitute appearances – in the league this season, otherwise starting every Europa League game.
Chelsea paid £23m for the player, and it is unlikely they will be able to recoup their expenditure.
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A loan deal with the option to buy may be the best chance the Blues have of flogging Zappacosta for the best price, and it appears technical director Marina Granovskaia is pursuing that avenue.
Italian newspaper Il Messaggero are reporting that Chelsea have accepted a loan bid from Lazio for Zappacosta, with potential for a £13.5m summer move.
The player’s departure could allow Sarri to link up with full-back Elseid Hysaj for a third time.
The Albanian has played under Sarri at Empoli and Napoli, and it is believed the Italian tactician is keen on having Hysaj follow him once more.
Speaking last Friday, Hysaj’s agent said: “A transfer in January? In the summer he could have gone with Sarri to Chelsea.
“But [Napoli manager] Ancelotti openly told us that he needed him. We need to find a solution to the problem.
“He was among the best performing full-backs in Europe. If he is seen as an alternative, we will ask for a sale in January.”