The Blues were heavily linked with the 26-year-old defender during the summer, but they were unable to get a deal over the line.
However, the West London club could revive their interest at the turn of the year, considering Reece James is currently out of action with a knee injury.
James is believed to return before Christmas, but the Premier League giants may still want a new signing for the defence role.
Dumfries would be an ideal option with his attacking instincts and could be prised away for around €40m at the midway point of the campaign.
Man United were also said to be interested in the Dutchman last summer, but they are unlikely to revamp their interest this winter.
Dumfries has a contract at Inter Milan until June 2025.