Former SPL chief executive Doncaster is currently sharing duties with his Scottish Football League counterpart Longmuir.
Both want the top job, and the new organisation's six-man board will choose between them.
Doncaster said: "It's not a question of applying for the position. There are two acting chief executives and the board will be selecting one of those to take the new league body forward.
"Interviews will take place over the next 10 days or so but that's for the board to decide who they want to lead the organisation in future."
Longmuir said: "There will be a process over the next week or so where the newly-appointed board of the SPFL will make a decision. I will enter into that process wholeheartedly."
A deal to reunite the governing bodies has been proposed and faltered several times, and Longmuir has revealed that the merger was under threat until the last moment.
He said: "There was a point in time yesterday where the SFL board were not completely satisfied to allow the decision to be made.
"There was more time, more information, more co-operation required. Once we achieved that, it all began to develop."
The SPFL will have 42 member clubs after Rangers' full share was reinstated, and the Ibrox board plans to play a leading role.
Chief executive Craig Mather said: "This is the status Rangers should have and we look forward to playing a full and leading part in the rebuilding of Scottish football.
"That's what all of us, everyone who cares about the game, should be working towards. It is also important that Rangers' voice be heard because this club is too big and too important to be ignored."