Supervisory board chairman Manfred Schneider favors Peter Terium, the dark horse who emerged as frontrunner last week, but municipalities that control about a quarter of RWE's shares are pushing for management board member Rolf Martin Schmitz, they said.
There is no solution yet, one of the people said ahead of a supervisory board meeting on Monday.
Sources told Reuters last week that Terium, largely unknown in the public sphere, had beaten Schmitz and Leonhard Birnbaum in the race for the top job.
Terium, a 47-year-old Dutchman, has been with RWE since 2003 and has been CEO of Essent since he led RWE's acquisition of the Dutch utility two years ago.
This would not be the first time RWE has picked a dark horse to lead the company. Grossmann led steel unit Georgsmarienhuette before being named CEO four years ago, and his predecessor Harry Roels previously worked at Royal Dutch Shell
RWE, which declined to comment, is looking for a leader to succeed Grossmann when his contract runs out next year and to help Germany's largest power producer transition to a post-nuclear era.
The German government permanently shut eight nuclear power plants early on in the Fukushima nuclear crisis in Japan, and decided to phase out nuclear power by 2022, overturning legislation that had extended the lifespan of the country's 17 nuclear plants by decades.
The country's four big utilities -- RWE, E.ON
Shares of RWE were up 0.3 percent at 32.61 euros by 4:55 a.m. EDT, slightly underperforming the STOXX Europe 600 Utilities index <.SX6P>, which was up 0.5 percent.
Taking the helm at a time of turmoil in the German energy industry, Grossmann's successor will face the unenviable task of setting a new course for overstretched RWE.
Analysts say RWE could be one of the hardest hit by Germany's nuclear exit because it is less active in other markets than main rival E.ON, and relies heavily on nuclear and coal-fired power generation.
RWE is due to publish first-half financial results on Thursday, a day after E.ON.
Smaller peer EnBW and Vattenfall have published financial results that were hit by writedowns and provisions related to the nuclear exit.
RWE is relatively weak in gas and renewable production. But investing in expansion there would require a lot of cash and RWE already has more than 27 billion euros ($38 billion) of debt.
The company has been hit by credit rating downgrades and has said a capital increase, merger with a peer and more divestments were among its options to avert further cuts.
Analysts estimate it needs to raise about 4 billion euros in addition to an 8 billion euro disposal program it announced.
A new CEO will also have to fix RWE's image after Grossmann, called nuclear Rambo by some critics, stubbornly fought the German government's push for a nuclear exit.
He argued a quick shutdown would cost energy-intensive industry dearly and could threaten Germany's industrial base, even when he was hit with harsh criticism at the company's annual shareholders' meeting in April.
($1 = 0.705 Euros)
(Reporting by Tom Kaeckenhoff and Matthias Inverardi; Writing by Maria Sheahan; Editing by David Hulmes)