Driscoll was a coach at Stamford Bridge under the club's two most successful recent managers, and took up his new role at Anfield this season.
"All the managers I've worked with have their own unique traits - but Brendan has the best mix," he told the club's website.
"I still have strong relationships with many of the managers I've worked with, and so I mean no disrespect, but Brendan definitely has a unique combination of all the best traits I've seen.
"Carlo Ancelotti was very humble and showed a lot of humility - I see that in Brendan. I also see the man-management style of Guus Hiddink and obviously the methodologies of Jose [Mourinho] in him. For me, I feel very privileged and lucky to now be working back with him."