"It's entirely the purview of the prime minister," he said. "So that will be up to Bill to decide."
Mr Muller endorsed Tauranga MP Simon Bridges over Paula Bennett for the role of deputy prime minister.
Mr Muller said he believed his influence over other MPs was "overstated by the media".
"I'm just a guy who tries to have as good a relationship with as many people as possible," he said.
Mr Muller said that New Zealanders were looking for strong leadership, continuity and stability during a time in which the world was in "a heightened state of flux".
He described Mr English as one of the world's best finance ministers, and Mr Bridges as a young, dynamic man who was "a face for generational change within the party".
When asked about Mr Muller's chances of advancement, political expert Professor Raymond Miller of Auckland University said the MP was "pretty new" but had already developed an impressive background.
Today I am announcing my support for Bill English in his bid to become the Leader of the National Party and Prime...
Posted by Todd Muller MP on Wednesday, 7 December 2016