Both men have entered the final year of their current deals at the iPro Stadium.
Derby do hold a 12-month option on Martin, but are eager to avoid the risk of losing either as free agents at the end of the 2014/15 campaign.
Martin’s goals helped to fire Steve McClaren’s men towards the Sky Bet Championship play-off last season, while Keogh was a rock at the back.
Derby hope both will commit their long-term futures to the club – following the lead of Jamie Ward, who penned a new two-year deal on Thursday.
McClaren said in the Derby Telegraph: “We have got two or three to go.
“I think the club is looking to do something with Richard Keogh and Chrissy Martin.
“We cannot have players looking over their shoulder, we need them looking forward.”