Premier Chris Minns is backing a bid from Mr Franklin, a close friend, to become upper house president in a deal that would make it easier for Labor to pass legislation in the split chamber.
The president does not vote on bills, so the deal would effectively give Labor control of the Legislative Council.
The move has caused a schism in the NSW Nationals, with party leader Paul Toole describing the situation as "distressing" and saying it would be a betrayal of the coalition.
"I think many people in the party would actually see that as a very concerning situation ... and it could be seen as disloyalty," he told Sydney radio station 2GB on Thursday.
Mr Toole said he had spoken with Mr Franklin but was unable to secure an assurance that his party colleague would not nominate for the role.
"It actually takes us one vote down and that is the most distressing thing here," he said.
In a thinly veiled threat, he said any decision would be scrutinised by the Nationals' party room and state executive, which has the power to expel Mr Franklin from the party.
"We want to get on with the job of actually holding the government to account," Mr Toole said.
"When you're talking about every vote in the upper house, it's going to be tight. We need everybody on the floor."
The plum job of president comes with a $315,814 annual pay packet as well as numerous perks including additional staff, a car and driver.
Mr Franklin has not publicly spoken on the matter but was seen meeting with Nationals colleague Adam Marshall and former Labor MP Adam Searle at a bar near parliament on Wednesday.
The premier endorsed him for the role on Wednesday, saying he would instruct his own party room to elect a non-government member for the job.
The Greens, who have four members in the upper house, also favour electing a non-government member.
In the lower house, independent MP Greg Piper is expected to take the equivalent role of speaker.
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