What is known as Formula One's "Silly Season", a motor racing version of musical chairs, revved up early this year with speculation about Hamilton's future as well as that of sitting-on-the-sidelines Australian Daniel Ricciardo.
Out of contract at the end of this season, Hamilton may move to Maranello if the rumour mill - already in overdrive - is anything to go by, with the Daily Mail reporting Ferrari were set to offer him a 40 million pound deal.
The seven times world champion himself and Ferrari have denied talks, with the Briton indicating he was close to a new deal with Mercedes.
Coulthard, winner of Formula One's glamour race in 2000 and 2002, advised against betting on the 38-year-old going anywhere other than Mercedes or retirement, however.
"A lot of rumours," said Coulthard, between hands at a Red Bull/PokerStars event. "Lewis is at Mercedes or he retires.
"I don't see him anywhere in between, and it will come down to their development and his belief in that development path because he is here to win grands prix and world championships. He doesn't need to do a global tour.
"A lot hinges on the development of that car."
Arguably Formula One's most storied team combined with the sport's most successful driver of all time sounds like a motor racing match made in heaven, and a driver of Hamilton's calibre is always going to fire up the rumour mill.
"I think every single team on the grid would like to have Hamilton at one stage," admitted Ferrari boss Fred Vasseur ahead of Sunday's race. "It would be rubbish to not say something like this."
Despite the denials from the main players, Formula One's favourite parlour game has many more hands to be dealt before next season's grid is sorted.
What does the future hold for Ricciardo, now filling a role as Red Bull reserve after losing his McLaren seat to rookie compatriot Oscar Piastri?
Already there has been talk of AlphaTauri reserve Nyck de Vries not lasting the season, with the Dutch driver yet to score a point in five races and Red Bull junior driver Liam Lawson making a strong case to replace him.
"It doesn't really come as a surprise, I think that’s part of our industry and world, and ultimately it comes down to performance and delivering on track," De Vries told reporters this week.
There has also been some murmuring about the form of American Logan Sargeant at Williams and his future beyond the season.
Over at Mercedes Mick Schumacher, son of Germany's seven times world champion Michael, is also looking to get back into a race seat after whiling away this season as a reserve.
There was even some speculation that retired four times world champion Sebastian Vettel, who made an appearance in the Monaco paddock on Friday, could be a stand-in when Canadian Lance Stroll was injured pre-season.
"The silly season has started early," declared Coulthard, conscious of how much can depend on the spin of a wheel in Monte Carlo.
"Before the season has even finished."
