The Spanish full-back, who spent last season on loan at Real Betis, still has a year left on his current contract with the Gunners.
He has been linked with a move back to the La Liga club, but the costs of pursuing a permanent deal are proving to be a barrier for Manuel Pellegrini’s team.
Bellerin is keen to head back to Betis and Arsenal understand the player’s desire to join the Spanish side.
It had been suggested that Arsenal could agree to terminate Bellerin’s deal to let him return to Spain and sign for Betis.
However, that is not a step that Arsenal are considering taking at the moment and they are looking for a cash offer for Bellerin.
The Gunners could reassess the situation late in the transfer window if Bellerin is still on the books.
Bellerin had a successful spell at Betis last season and helped the club to win the Copa del Rey.