Klopp last month named Gerrard as his preferred successor at the English Premier League club, but Beale confirmed it's not on the Rangers manager's mind. Speaking to the Liverpool Echo, he said: "We have not spoke about it. It's a compliment of course, but at this moment in time, Liverpool have the best manager for them.
"As a supporter of the club, Steven being a passionate supporter, we don't just support the first team, we follow it through to the U23s and 18s and we have watched some games together.
"We know what is going on at all the youth teams. He is the biggest Liverpool fan and at this moment in time, if he had to choose a manager, it would be Jurgen Klopp.
"I don't think Steven is looking too far ahead, it is a big job and obviously that is the dream - or rather, the aim - for him long term to manage the club.
"But I think Steven would say himself, right now, the best manager for Liverpool Football Club is Jurgen Klopp. Long may that continue."
Beale was previously head of coaching at the Liverpool Academy before moving to Glasgow to join Gerrard.