Kop icon Gerrard's managerial stock has soared after leading Rangers to a first Scottish Premiership title in a decade.
And Kuyt, who has had a spell with Feyenoord as youth coach, has declared his ambition to be part of a managerial dream team at Anfield.
"He is a child of the club, and he spent his entire playing career with Liverpool.
"Hopefully he will go on to experience similar levels of success as a manager.
"I get on very well with him, and we are still in contact with one another from time to time.
"If he wanted me to be his assistant I would like that a lot.
"In principle I see myself going on to work as a head coach, but there are always exceptions.
"And this would certainly be one of them."