Rosberg, 31, announced his retirement on Friday, just five days after winning the Formula One drivers’ title for the first time – an achievement he said completed his ambition in motorsport.
Valtteri Bottas of Williams, former world champions Sebastian Vettel and Fernando Alonso and Mercedes reserve driver Pascal Wehrlein have all been mooted as candidates to replace Rosberg.
“I think we should have a decision before the end of the year. We’ll give an unexpected Christmas present to one of the drivers,” said Mercedes non-executive director Niki Lauda.
“We certainly need a driver for the first test of the new car in February but I can assure you it will happen earlier because, whoever it is, we have to train them on the simulator, train him into the team.”
Rosberg, who emulated his father Keke by winning the drivers’ title, explained his decision to retire by saying: “I have climbed my mountain, I am on the peak, so this feels right.”
Lauda revealed his surprise at Rosberg’s move and revealed that he failed in an attempt to change the German driver’s mind.
“I was really surprised because normally I think all kind of things can happen but this was never on my radar,” he added
“I called him and really wanted to make sure it is not a quick decision that you might regret, and to my question of how sure are you, he said: ‘1,000 per cent’. Then I knew that it is over.”
Lauda confirmed at the weekend that Mercedes would not punish Britain’s Lewis Hamilton for his disobedience of team orders in the season-deciding Abu Dhabi Grand Prix last week.
Hamilton attempted to pressurise Rosberg into being overtaken by driving slowly when leading his team-mate at Yas Marina and ignored requests to speed up from nervy Mercedes chiefs. Rosberg held off Vettel to finish second and clinch the title.