Arsene Wenger's club have infamously failed to win a piece of silverware since the 2005 FA Cup and that wait for success looks set to continue this season.
Robben's Bayern Munich are well placed to dump Arsenal out of the UEFA Champions League last 16 after a first leg win in England on Tuesday.
And the former Chelsea star is unsure how long Wilshere will hang around, as he is quoted as saying in the Daily Star on Sunday: "I don't know if Arsenal can keep him if they are not winning things.
"It's always difficult to judge that about another player.
"But you can see that Wilshere is a very big talent and he is only young still. He's just 21 years old. He will definitely be a big player."
Wilshere signed a new long-term Arsenal contract in December but that has still not stopped speculation about his future.
However, the England international is viewed as a future captain of the Gunners and manager Arsene Wenger has never made any secret about the midfielder's leadership qualities.