Lampard was appointed as the Championship club's new manager on Thursday, signing a three-year contract at Pride Park.
With Terry having left Aston Villa in the wake of their play-off final defeat, there have been suggestions the former Chelsea captain could be a target for Derby.
However, Lampard has denied there have been any discussions about bringing the defender to the club.
"I haven't spoken to John," he told a news conference. "I got a message this morning. At the moment he's in Greece on holiday.
"There are conversations ongoing across the board; that isn't one of them. These conversations start now. John's had a great career but we'll concentrate on what we want to do here."
Former England star Lampard, who retired from playing last February, also denied receiving offers from more high-profile clubs before opting to move to the Rams.
"No, I didn't," he said. "I had other conversations, I wouldn't go as far to say offers. This is the outstanding offer and hence why I'm here."
The 39-year-old also insists he will have his own personality as a manager, having worked with some of the world's finest coaches in his playing career, including Jose Mourinho, Carlo Ancelotti and Guus Hiddink.
"I had the pleasure of so many great managers; I'm not a clone of any one manager I had," he added. "I saw what I thought was the good, and the bad of them, I'll make my own judgements. I'll be open."