The 19-year old is reportedly frustrated with the lack of first team opportunities with the Gunners.
Last season, the Englishman made two EFL cup appearances off the bench for Arsene Wenger's side.
Willock is out of contract next month.
And The Mirror reports that the London-born teenager has already flown to Portugal to discuss terms with Benfica.
Last year, Wenger spoke highly of Willock to the London Evening Standard.
"Chris is a very gifted player with natural strength and natural talent," said Wenger
"He has what you do not find very easily.
"He can have a go at people, can get past people in one on ones. We forget sometimes that the basis of team sport is to first be strong one against one and Chris has that quality.
"I would be very comfortable to play him now.
"But, of course, there is a lot of competition for places because there are players like [Theo] Walcott, Alexis [Sanchez] and [Danny] Welbeck in front of him at the moment."