John Bolton (2005 file photo) (Dennis Cook/Associated Press)

“Well, he hasn’t talked to me yet, so we will wait and see what will happen. I’m honored anybody would say that. But I think it’s presumptuous for people in that position to be accepting or not,” said Bolton.

Bolton said Republicans should focus on selecting the right candidate first before thinking about cabinet positions.

Gingrich joined AEI within three months of stepping down from Congress and remained at the think tank until earlier this year. Bolton joined AEI as a senior fellow following his position as the U.S. permanent representative to the United Nations from 2005 to 2006.

Bolton has not endorsed Gingrich and would not likely do so unless Gingrich won the Republican nomination given that he is in conversation with multiple GOP candidates on an array of foreign policy issues.

AEI and the Heritage Foundation co-hosted the last Republican debate Nov. 22 on foreign policy and national security.