Craig says he would "be willing and able to do whatever [Hogan] wants," but the county executive's office declined to speak further on the issue Monday.
"Governor-Elect Larry Hogan has not officially announced his transition team," Craig's spokeswoman Sherrie Johnson said via email. "Mr. Craig will call you once the announcement has been made officially."
Hannah Marr, spokeswoman for Hogan's campaign, would neither confirm nor deny Craig's role in the transition.
"We have not released any information" on the team, she said Monday, explaining more details are expected to be publicized within a week.
Hogan is firming up his transition team in preparation for taking over from outgoing Gov. Martin O'Malley in mid-January. Three people reported to be involved are Lt. Gov.-elect Boyd Rutherford, Baltimore businessman Jim Brady, who ran transitions for former governors Parris Glendening and Robert Ehrlich, and Hogan campaign manager Steve Crim.
Craig, who leaves office Dec. 1 after serving as Harford County's executive since mid-2005, lost to Hogan in the June gubernatorial primary election and then campaigned actively for Hogan leading up to the general election.
He said over the weekend he was told he would serve on the team, but was still awaiting instructions.
Craig was with Hogan on election night Nov. 4, as Hogan awaited returns and then declared victory.
On the afternoon of Oct. 30, Craig escorted Hogan around Bel Air and that evening the two visited Craig's hometown of Havre de Grace for the city's annual Halloween parade.
Doug Donovan, Erin Cox and John Fritze of The Baltimore Sun contributed to this story.