The highly-rated midfielder, 20, has been on Arsenal's books since 2006 but he has not been able to break into Arsene Wenger's squad.
He has spent the last two seasons out on loan, most recently with Dutch club FC Zwolle.
Sparta are now keen to keep Van den Berg in his homeland and will take a look at him in a match against Young NEC Nijmegen this week.
"He has already trained with us a couple of times," Sparta technical director Richard Grootscholten told ELF Voetbal.
"He can play in a match so we can see what he can offer us. That's what trial matches are for, isn't it?
"He may be a reinforcement for Sparta. We of course know that Vincent is a good player but he was out for a while.
"We will decide later on if we are going to offer him a permanent contract. I don't know when that will happen, we don't want to put a timeframe on it.
"Let's wait and see what happens."