Lampard has taken his first steps into the world of management by agreeing a three-year contract at Pride Park, tasked with mounting a promotion push on a reduced budget compared to predecessor Gary Rowett.
The former England skipper has worked under a number of high-profile names during stints at Chelsea and Manchester City, including eight-time title winner Mourinho, which Davies believes will stand the Blues legend in good stead.
"He has worked for some of the biggest managers in the game," he told the club's official website. "Even if he picked up one thing from each of those, it is going to be a lot more than a lot of us could have got and his insight is going to bring a lot.
"If he does pick up the phone - I'm not saying the manager will need any help at all - but I'm sure if he picks up the phone to Jose or any of the others for advice, I'm sure they would be very happy to help him.
"I've played against him many times and he is just a good person. He is a winner on the pitch, so he's not going to not tackle you, because he wants to win games, but he is always a gentleman.
"He's honest and a nice person to talk to. As a young player to look up to he was definitely one that always did the right things on and off the pitch."
Lampard has spent time working as a pundit since ending his playing career in 2016.