Mary Lou McDonald looks set to become the next Sinn Féin President after a number of other contenders ruled themselves out of the race.
Pearse Doherty and Michelle O'Neill say they will not challenge for the post.
Gerry Adams announced his intention to step down after 34 years as Sinn Féin leader at the weekend.
Ms McDonald now looks like the clear favourite to replace him, but Mr Doherty says she might not go unchallenged.
He said: "We don't do coronations. The Ard Fhéis will decide, certain individuals have decided, including myself, that we won't be contesting that position.
"But our party is very big and any member of the party can put their name forward for this position.
"The Ard Comhaire are going to meet over the next month. Every person should be given space to consider whether they believe that he or she is the person to go forward."