The 23-year-old is attracting interest from Sevilla and Valencia, according to 'El Gol Digital'.
Oxlade-Chamberlain has started just three Premier League games for Arsenal this season and the La Liga duo are eyeing up January loan moves for the winger.
The player himself has expressed a desire to play more football, but Wenger hopes that the former Southampton midfielder will stay.
Wenger previously said: "...you buy a young player at 17 years of age, you spend a lot of money on him, so then you would like him to stay. I think his place is here.
"I rate him as a player and I hope he will show he can have a stable position in the team until the end of the season".