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According to Calcio Mercato, the Gunners have held “positive talks” with the Argentina international and a transfer to the Emirates Stadium could follow.
Banega has reportedly put a number of top European clubs on high alert after expressing the desire to leave Sevilla this summer.
The 29-year-old is said to have grown disillusioned at the La Liga side following the departure of director of football Oscar Arias, who brought him to the club from Inter Milan.
Meanwhile, Arsenal are believed to have agreed a deal to sign Sampdoria midfielder Lucas Torreira.