The 28-year-old, who was awarded the PFA Players' Player of the Year gong last night, has refused to cement his future at the Emirates, sparking speculation that he could be on his way out of the club.
"Yes he is vital to success," the London Evening Standard quotes Gullit as saying. "Arsenal need to win trophies and I think Van Persie wants to and he knows if he wants to become one of the legends of football he needs to win trophies and he will ask Arsene Wenger to strengthen the squad. The team need to give him help.
"He is a class act and I can't see any reason why he can't score many more goals, if Arsenal can keep hold of him of course, which they really need to do."
Van Persie has netted 27 goals for the Gunners so far this season.