The 26-year-old Italian international had been linked multiple times with I Nerazzurri when Antonio Conte was coach and their interest has not waned despite the recent departure of their former tactician.
According to La Gazzetta dello Sport, Chelsea want €20 million for Emerson but Inter are confident that his price can be lowered because his contract expires in June 2022.
Napoli are also searching for a left-back and they too have an interest in the Chelsea defender but Il Biscione are expected to have the upper hand in the deal.
Emerson Palmieri featured in 15 competitive matches throughout the 2020/21 season for the west London club including just two appearances in the English Premier League. Despite this, he was still selected by Italy coach Roberto Mancini for the upcoming European Championship.
Meanwhile, Inzaghi was appointed as coach of Inter on Thursday after coaching Lazio for five seasons.