Sanchez, who joined Arsenal from Barcelona in a £30m move last summer, shared a Premier League pitch with Vargas on Boxing Day last year as the Gunners beat Queens Park Rangers 2-1 at Loftus Road.
Vargas spent the 2014-15 campaign on loan at QPR from Napoli, scoring three goals in 21 Premier League games.
He did not excel with the Hoops, but Sanchez seems to think he could succeed at Arsenal.
According to the Metro, Alexis has made a request to manager Arsene Wenger, imploring him to sign Vargas this summer.
The Metro claim it would cost Arsenal around £11.3m to grant Sanchez’s ‘transfer request’.