Spanish side Valencia are keen on the centre-back although are yet to bid.
Amid the reports of his availability, Premier League side Everton should test Arsenal's resolve by meeting their asking price.
The Toffees may have signed Michael Keane from Burnley, but they have lost Argentina international defender Rafa Funes Mori to a serious knee injury which will cause him to miss the entire 2017/18 season.
Everton have veterans Ashley Williams and Phil Jagielka available, but 26-year-old Gabriel would add another important option as they look to balance Premier League and Europa League football.
Arsenal can afford to let Gabriel go after Rob Holding's emergence last season, which saw him restricted to only 15 league starts.
The Brazilian has Premier League and Champions League experience having signed for the Gunners in January 2014 from Villarreal.
He is an ideal player for Everton to throw into the mix to compete for a starting spot, playing with the same aggressive style as Funes Mori.
Gabriel needs a move to keep his career moving forward and avoid a season on the sidelines having fallen out of favour, and Everton's ambition could convince him to sign.
The only problem would be whether Arsenal now consider them too close a competitor to do business with.