The Arsenal academy product is believed to have been deemed surplus to requirements this summer following the signing of Sead Kolasinac and several sides are believed to have expressed an interest in the player.
West Brom are one of them, though they are believed to have baulked at Arsenal's £12million asking price.
Watford and newly-promoted Newcastle have also been heavily linked with moves for Gibbs, with Arsenal looking to sell some players to balance the books after the club-record signing of Alexandre Lacazette from Lyon.
Amongst those expeted to leave are Calum Chambers, who is the subject of a £16m bid from Crystal Palace, Jack Wilshere, who is being chased by Sampdoria and Wojciech Szczesny who is closing in on a £10m move to Serie A champions Juventus.