The Holland international joined the Gunners in 2023 from Ajax and has a deal until 2028.
BBC Sport says Arsenal want to reward Timber for his consistent form since returning from a knee injury suffered two years ago.
Timber recovered last season, making 51 appearances to establish himself as a first-choice for manager Mikel Arteta.
Arsenal are turning to upgrade and extend Timber's deal just days after securing William Saliba to a new contract.