However, according to the London Evening Standard, the 67-year-old has not yet made up his mind and will use the international break to consider all options.
It has been widely reported that the Frenchman, whose contract expires in the summer, wants to stay at the Emirates amid protests from disgruntled fans.
During Saturday's match, a banner calling for Wenger to leave was flown over The Hawthorns, but another was spotted shortly afterwards demanding more respect for the manager.
Arsenal face missing out on a top-four spot this season as they currently sit sixth in the Premier League table, six points adrift of fourth-placed Liverpool, but they have two games in hand.
The Gunners have lost six of their last nine games in all competitions.