Meanwhile, Barcelona are thought to be considering Chelsea's Cesar Azpilicueta as a potential target.
The Catalan giants are in the market for a new full-back after Juventus sealed a deal for Dani Alves yesterday.
Barca sporting director Robert Fernandez had suggested earlier this month that no formal approach had been made for Bellerin.
He said: "I haven’t raised [Bellerin] at this point.
''He’s a fantastic player who we know because he grew up here but at this time I’m not raising anything in this regard.
"Aleix Vidal was signed [last summer] thinking Alves could go. We trust in him.
"He was having a fantastic season at Sevilla and we have the emergence of Sergi Roberto. Douglas? I want him to play.”
The Gunners finished runners-up to Barclays Premier League champions to Leicester last term.
Arsene Wenger has already signed Granit Xhaka for £30million this summer.
