The 'Gunners' failed with a cheeky attempt to bring the England man to the capital during the summer but are thought to be keen on revisiting the move.
Arsene Wenger is known to be a huge fan of the former Liverpool man and asked for the 22-year-old to be included in any deal to take Alexis Sanchez to the Etihad during the summer.
That move never came to pass, though English publication 'The Daily Mail' reports that Arsenal will attempt to revive the deal in January.
Pep Guardiola is unlikely to be tempted by the offer though, with Sterling having scored 10 goals in 15 games so far this season and becoming a key member of the City side.
City are expected to return with a fresh bid for Sanchez when the transfer window re-opens, though it makes no sense from their point of view to include Sterling in any deal.