The world number two is in the habit of shrugging off the weight of expectations with his 2012 US Open and 2013 Wimbledon triumphs.
He is also a five-time Australian Open runner-up but the unique challenges of Paris’s red clay have so far stumped him at the semi-final stage on three occasions.
On Friday he gets another opportunity to make a first British breakthrough since Bunny Austin reached the final 79 years ago.
Only then will the 29-year-old ponder a title last won by a compatriot when Fred Perry triumphed in 1935.
“I think at this stage of my career to do things that I have never done before is nice,” said Murray as he contemplated reaching the final of all four Slams.
“That’s one of the things that motivates me and drives me. That’s why my results on clay over the last couple of years have been really special to me because I never expected that really, and it had come in the latter stages of my career.”
Murray came into Paris having defeated world number one Novak Djokovic in the final of the Rome Masters but under a cloud following the end of his coaching relationship with Amelie Mauresmo.
His campaign was almost scuppered at the first hurdle when he had to fight back from two sets down to defeat 37-year-old Radek Stepanek. He then needed another five sets to beat French wildcard Mathias Bourgue, the world 164.
Since then, Murray has been relatively untroubled, seeing off big-servers Ivo Karlovic and John Isner in straight sets before defeating home hope Richard Gasquet from a set down.
– Rain favours –
He has even seen the torrential rain act in his favour.
Having played his last-16 match against Isner on Sunday, he didn’t return to the courts until Wednesday to face Gasquet before enjoying a free Thursday.
In comparison, Djokovic played his last-16 round over two days on Tuesday and Wednesday and was up against Tomas Berdych in his delayed quarter-final on Thursday.
Djokovic defeated Murray in a classic five-set semi-final 12 months ago, but this year they can only meet in the final.
In his previous two semi-finals, in 2011 and 2014, Murray lost to Rafael Nadal in straights.
However, Nadal withdrew from the tournament with a wrist injury last week while another threat, Roger Federer, opted not to play at all to rest a back injury.
But that won’t mean he will under-estimate Wawrinka who stunned Djokovic in last year’s final.
The 31-year-old Swiss is the oldest semi-finalist in Paris since Jimmy Connors in 1985.
Murray leads their head-to-head 8-7 but Wawrinka has won their last three meetings.
The third seed has also won both their tour claycourt meetings — in Rome in 2008 and Monte Carlo in 2013.
Like Murray, Wawrinka also needed five sets to get through his opener against Lukas Rosol, but has dropped just one set since.
However, Wawrinka insists that Murray is the favourite to win Friday’s clash, even claiming that the Scot is in a different class despite both men having claimed two Grand Slam titles apiece.
“If you were to compare our two careers he’s well ahead of me given all the titles, the finals, number two in the world, and he has so many Masters 1000, as well,” said Wawrinka who was also the 2014 Australian Open champion.
“As I keep on repeating, he’s in the ‘Big Four’ (with Djokovic, Federer and Nadal). Maybe he has fewer titles than the other three, but he’s always been with them during the semis, the finals. His career is very, very impressive.”
Wawrinka has a career haul of 14 titles, including his two majors and one Masters.
Murray has racked up 36 titles with two Grand Slams and 12 at the Masters level.