However, he added that if he continues to warm the bench under new Blues manager Maurizio Sarri, he will have to consider leaving the Premier League club, per Corriere dello Sport (h/t ESPN.co.uk):
"I want to try to give the coach food for thought, also because my objective is to remain in the reckoning for Italy. Inter sought me in the summer, but I am happy here. If I were not to play much, though, I'd think about [leaving]. Nobody likes being on the bench."
Zappacosta, 26, joined Chelsea from Torino last summer for £23 million.
He was largely a back-up under former boss Antonio Conte, with 10 of his 22 Premier League appearances last term coming from the bench.
And in three English top-flight matches in 2018-19 under Sarri, the Italian defender has yet to make it onto the pitch.
The former Napoli manager looks to have decided upon Cesar Azpilicueta as the starting right-back in his 3-4-3 system, hardly a surprise given the Spaniard's remarkable consistency over the past seven seasons at Stamford Bridge.
Squawka Football @Squawka
César Azpilicueta is set to make his 200th Premier League appearance for Chelsea today; he has played 82.8% of all possible league minutes since joining the club. • 200/230 games • 17,136/20,700 minutes He's only missed 90 minutes since the start of the 2016/17 season. 🔵 https://t.co/6Mv5QU44S0
That does not mean Zappacosta will not be afforded game time this season.
As well as the Premier League, Chelsea will be looking to compete for the FA Cup, League Cup and UEFA Europa League in 2018-19, and Sarri will need to use his full squad in the campaign's busy periods.
However, it is unlikely Zappacosta will be happy to only play a significant role in the cup competitions.
He was a key part of Torino's first team before making the switch to Chelsea and he will likely look to force a move in January if he is only used sparingly by Sarri in the first half of the season.