The 24-year-old is out of contract with the Villans next summer, and Agbonlahor, who committed himself to the club until 2018 recently, wants Delph to follow suit.
"For me, as a close friend and team-mate, I'd love nothing more," he told The Mirror.
"Fabian does a lot of extra training out of football. He is the most dedicated player I have seen so far since I have been here.
"He would rather do extra training than go for a beer. That is his mentality, he wants to achieve big and go far."
Former Leeds United youth Delph earned his first two caps for England recently after continuing his impressive form for Villa this season.