The 37-year-old took his first steps into management ahead of the current campaign, assuming control of the club's U18s team.
The young Reds subsequently avoided defeat in the league until February and, though the mid-season promotion of a number of players to the U23s has led to a slight dip in form, Gerrard has enjoyed a largely impressive start to life in charge.
For Ayestaran, who oversaw some of the midfielder's finest performances during his time at Anfield as Rafael Benitez's assistant, this early success in the dugout comes as no surprise.
And, though the Spaniard warned of the challenges posed by a transition from playing to management, he is in no doubt Gerrard is capable of pulling it off.
He said in Back at Melwood... with Pako Ayestaran, which premieres on LFCTV on Monday April 2: "When we arrived here, we were quite lucky because when you are trying to build a squad you have to look to the professional football qualities, and the human and personal values.
"At that time, we had many players that were, as I say, full-time professionals, and Stevie was one of them. He had all the football qualities but he had these personal values as well that made him get the best from his qualities.
"Now, I don't know him as a manager, but he has to try and put into practice the things he's trying to learn [and] make mistakes, because it's the only way you can improve.
"Another thing I think is important once you leave your football career is you have to forget what it meant to be a football player and think as a manager.
"I think he is going through this process at the moment but he has all the qualities and attributes that, if he gets the best from this learning period, I am sure he can become a good manager in the future."
Tune into LFCTV at 5.45pm BST on Monday April 2 to watch the premiere of 'Back at Melwood... with Pako Ayestaran'. An extended version of this unmissable show will be available on demand on LFCTV GO 24 hours later. Head to liverpoolfc.com/watch for more details.