The Manchester City full-back, 30, has had a turbulent few months after breaching coronavirus rules four times.
And the Serie A giants are ready to pounce in the hope a fresh start for Walker abroad could tempt him into an Italian switch.
England defender Walker started the 3-0 Premier League win over Arsenal at the Etihad on Wednesday night.
But City boss Pep Guardiola admitted he has spoken to the right-back about his behaviour during the lockdown which included hosting a sex party at his flat.
Walker issued a statement to explain his actions but City said they would launch an internal probe into the first incident.
Despite Inter’s interest, Guardiola’s City are in no rush to sell Walker, who has won two Premier League titles since his £50million move from Tottenham in 2017.