The Citizens are believed to be in the market for a new left-back, amid suggestions that Oleksandr Zinchenko is looking to leave the club in search of regular first team football.
Pep Guardiola regards Brighton & Hove Albion's Marc Cucurella as his primary target, but it is thought that the Citizens are unwilling to meet the 23-year-old's £50m price tag.
According to The Scotsman, Man City could turn their attention to Tierney if they fail in their attempts to lure Cucurella to the Etihad Stadium.
The report adds that the 24-year-old Scotland international is admired by Guardiola, but the Premier League champions could face competition from La Liga giants Barcelona and Real Madrid for his signature.
Despite suffering with a number of injuries during his three-year spell at the Emirates Stadium, Tierney is valued as an important member of Mikel Arteta's first-team squad.
The former Celtic man, who has recorded four goals and 12 assists in 87 appearances for the Gunners across all competitions, still has four years remaining on his contract.
Wolverhampton Wanderers' Rayan Ait-Nouri, Crystal Palace's Tyrick Mitchell and Hoffenheim's David Raum are three more left-backs who are allegedly on Man City's radar.