Lampard was named Derby's new coach last week just a few weeks after Gary Rowett left to join Stoke City.
The former Chelsea midfielder will be hoping to build on their play-off finish in what will be his first managerial job.
Davies admits he has plenty of respect for the former England international and he believes he could get advice from Mourinho ahead of his debut campaign.
He told the club's official website: "He has worked for some of the biggest managers in the game. 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.
"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."