Gaitan has been linked with a move to Old Trafford on numerous occasions and Louis van Gaal is still keeping track of the midfielder’s progress.
The Argentine international has £26m buyout clause but Vitoria wants the club’s directors offer him a new deal.
“Gaitan’s renewal is something beyond my duties,” he told A Bola.
“He is firmly rooted in this club, part of our family and it’s good to have a player like him. He’s essential to Benfica.”