The Spanish midfielder previously worked with Gunners boss Unai Emery at Sevilla and was linked with a move to the Emirates Stadium this summer, only to remain in La Liga.
However, The Mirror reports that Arsenal are planning to return for Banega in January and are willing to trigger his £18m release clause in order to secure his services.
Banega would be available on a free transfer next summer, but Arsenal are understood to want to beat any other interested parties to the punch by signing him in January.
The future of Ramsey remains uncertain, with the Wales international currently in the final year of his contract at the club, forcing the Gunners to look at potential replacements for the long-serving midfielder.
Any deal for the 30-year-old Banega could be the first under new Arsenal head of football Raul Sanllehi.