Unai Emery, who replaced Arsene Wenger at the Emirates in the summer, worked with Banega in La Liga and is keen to bring the Argentine to north London.
Banega, who has 65 international caps, is settled in Seville and enjoying his role in Pablo Machins team but is tempted by the prospect of a switch to the Premier League.
Emery is putting pressure on Arsenal to meet his £20million buy-out clause and Mundo Deportivo say Banegas agent is currently in London, where he will seek talks with Arsenal.
Gunners boss Emery views Banega as an ideal replacement for the outgoing Aaron Ramsey.
Wales midfielder Ramsey has spent over a decade at the Emirates but is set to leave the club at the end of the season after talks over a new contract broke down.
Emery has made an assured start to his role as manager of Arsenal, taking the club into the top four of the Premier League and impressing in the Europa League.
But the Gunners have dropped to fifth after drawing to Brighton on Boxing Day and face leaders Liverpool this weekend.
Ahead of Arsenals trip to Anfield, Emery has backed Liverpool to go unbeaten throughout the 2018-19 season.
They can do that because they are doing it at the moment, he said.
We played against Liverpool three [seasons] ago with Sevilla in the final of the Europa League and I look at this progress and they are a very good example.
This progress is also one example for us, now, in our moment. But we need to be very, very demanding of ourselves to do this step quickly in our way.
But we need also time and sometimes the patience is very important for us.