The England international is yet to agree a new deal with the club and with only a year remaining is likely to be sold this summer with Anfield understood to be his most likely destination.
Jurgen Klopp is a known admirer and is set for a busy summer as he attempts to build a squad capable of challenging both in the Premier League and in Europe where the Reds are back in the Champions League after a two-year absence.
Arsenal are set for an overhaul of their own and are under pressure to cut their wage bill in the wake of the Premier League’s new cost control measures that are coming into force this summer.
The rules say that a club’s wage bill should not be more than £7m more than it was in 2016-17, or £19m more than from the 2012-13 season.
If it does increase beyond that limit, the money can only come from external sources such as player sales, ticketing or commercial money, rather than Premier League central funds.
If Arsenal’s wage bill does jump by as much as they want it to with proposed new deals for Alexis Sanchez and Mesut Ozil, they are unlikely to make up the money through commercial or ticketing or TV money for next season, not least because they will be playing in the Europa League, not the Champions League.
This means the money will have to be found in player sales this summer, not just of fringe players, but first-team players too.
Olivier Giroud is another who could follow Oxlade-Chamberlain out with Napoli joining Marseille and West Ham monitoring his situation. Jack Wilshere is another who could leave after spending last season on loan at Bournemouth but his wages may prove a stumbling block to a permanent move.
There are plenty of fringe players likely to depart, including Calum Chambers, Wojciech Szczesny, Chuba Akpom, Kieran Gibbs, Lucas Perez and Carl Jenkinson but Hector Bellerin is set to stay with the Gunners telling Barcelona that the Spanish right back is not for sale at any price.