Before them, only Briton Graham Hill managed the feat, winning from 1963-65.
Seven-time champion Michael Schumacher won the race five times in all, but never three times in a row.
All of which leaves Rosberg on the cusp of a potentially famous achievement as he attempts to rein in Hamilton, who has won three of this year's five opening races.
Last year, Rosberg triumphed ahead of Hamilton after a controversial off-road excursion during qualifying left the Englishman fuming amid a variety of conspiracy rumours.
It set the tone for an acrimonious period of rivalry between the two, a spell that Rosberg would be happy to usher in again if it goes with another memorable Monaco win.
Hamilton, however, has other ideas as he strives for only his second win on a circuit he loves.
"I am more than ever looking forward to this one, I really am," said Hamilton, whose future with Mercedes is expected to be confirmed this weekend. "I've not won in Monaco for a long, long time - this is going to be my third chance with this great team and with a great car."
The race will be important for Manor Marussia as it marks the anniversary of their only points-scoring finish, achieved last year when Frenchman Jules Bianchi came home ninth. Bianchi remains in hospital in Nice recovering from his life-threatening crash during the Japanese Grand Prix last October.
Pirelli will this weekend give the teams a new compound of super-soft tyres, designed to help allow overtaking in the classic 78-lap contest.
- AAP