The news emerged that the Coleraine man is in the frame after current Dr Who, David Tennant announced he will depart the role after the next series.
Tennant, who also has strong family connections to Londonderry, took over the role from Christopher Eccleston in 2005.
Nesbitt, acclaimed for his roles in Murphy's Law, a recent portrayal of the classic Jekyll and Hyde as well as portraying Londonderry political figure Ivan Cooper in Sunday, emerged as a front runner this morning.
Other names mentioned for the role are David Morrisey who will appear in a Doctor Who Christmas special entitled The Next Doctor, and newcomer Russell Tovey, who appeared in last year's festive episode.
Irish bookmaking giant, Paddy Power has named Nesbitt as third favourite on his list of replacements for the current Timelord. Paterson Joseph is quoted at 3-1, David Morrisey 5-1, James Nesbitt at 6-1 and John Simm at 8-1.