Robben saw first-hand the abilities of the England international during this week's Champions League encounter against his Bayern Munich side, as Wilshere emerged from the 3-1 defeat as one of the few positives on the night for the Gunners.
The first leg result at the Emirates Stadium has left Arsenal facing an uphill task to reach the quarter-finals, and anything less than a convincing victory in the return game next month will condemn Arsene Wenger's team to another season without a trophy.
The north Londoners haven't won a trophy since the 2005 FA Cup and that wait for success has already driven a number of stars to the exit door, and if it goes on much longer, Robben thinks Wilshere could be the next to go.
He told 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 deal in December, but even that move has done little to stop speculation about his future.