Muir, who came second in the 1,500m in Tokyo three years ago, will again compete this year in the hopes of sealing a first gold medal in Paris.
Three-time grand slam winner Murray has confirmed he will retire from tennis after the Games, having previously won gold on two occasions.
The Scot's first Games appearance was in Beijing in 2008, losing in straight sets to Lu Yen-hsun in the first round.
Four years later, Murray triumphed on home soil by beating Roger Federer at London 2012, beating the Swiss in straight sets in the final.
The Briton became the first male tennis player to win two Olympic singles titles when he beat Argentina's Juan Martin del Potro at Rio 2016.
Murray withdrew from the singles event at the most recent grand slam at Wimbledon, competing in the doubles alongside brother Jamie but going out in the first round.
Dan Evans will partner Murray in the doubles in Paris, with Muir praising the Scot's influence both on and off the court across his 19-year professional career.
"I think it's just he's been at the top for so long, and it's just been so nice to see him progress through everything," Muir told Stats Perform.
"He's had so many hard times and he's come back and he's fought so hard and he's been so patient and such a big sportsmanship person at the same time.
"I think he's just hugely inspirational, not just in the sport of tennis but through Scottish sports and also lots of other sports on the team as well.
"Just to see someone fight for so long and do so well, it's been so nice to see.
"So it'll be such a shame that we won't see more of him to come, but it's just so nice to be able to finish it with the Olympics - he's hugely inspirational person both on and off the court."
Fellow 1,500m hopeful Jake Wightman, who finished 10th at the Tokyo games, echoed Muir's words on Murray's glittering career.
"I think probably him winning Wimbledon for the first time is like a iconic moment within my sporting history, just because I'd watched Wimbledon most years and never seen a Brit perform anywhere near that level," Wightman told Stats Perform.
"You'd obviously had Tim Henman going to a certain point, but it had been an era of just watching [Rafael] Nadal and Federer for a long time battling it out.
"So to see somebody in Britain, a British athlete, being able to go and do that was, I think, something that we may not see for a long time."
The 28-year-old became the first Briton in 39 years to win the world 1500m title with a shock victory over Olympic champion Jakob Ingebrigtsen in Eugene last year.
His victory was even more memorable because his dad Geoff, the stadium announcer at Hayward Field, commentated on his run.
Wightman went on to earn 1500m bronze at the Commonwealth Games and 800m silver at the European Championships, but he suffered a foot injury at the start of this year and has since had shin and hamstring problems.
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He revealed he has taken the decision to miss the World Championships so as not to “jeopardise” his fitness for next year’s Olympics in Paris.
“Sadly I’m going to have to wait a bit longer for a moment like this…” he posted on Instagram, beneath a picture of him celebrating his world title.
“As a result of my injury I sustained in February, I’ve had to deal with several more set backs as I prepared to race this summer.
“I’ve always felt as though time has been on my side to overcome my problems fully, however it has finally run out.
“This means I’m sadly going to be unable to compete at Worlds which has been really gutting to come to terms with.
“Although I’m very disappointed not be able to try and defend my title, my focus has to be on getting my body rested and ready for 2024, to ensure I’ll be back performing at my best.
“The are some risks I could’ve taken to be on that Budapest start line, however the potential to jeopardise my Olympic year makes this the obvious decision.
“I’m currently taking some down time before starting my rehab, ready to be back running safely and pain free by the end of August.
“Big thanks to all my team and British Athletics who have worked really hard to try and give me every chance of competing.
“I’ll see you back on the start line soon.”
Wightman explained the succession of injuries he has suffered this year has prevented him from competing.
He said on the Scottish Athletics website: “After suffering shin and hamstring injuries, one after the other, I am just going to be too far off where I want to be on the start line at the championships in Budapest in August, so I am not going to be taking up my wild card as reigning champion.
“It all began with a foot injury earlier in the year which saw me miss the European Indoor Championships – and things went from there.
“It turned out to be more than just a bump in the road. After some discomfort in my Achilles from where I had been wearing the boot, I arrived in Flagstaff, Arizona, for training camp pain-free.
“However, a couple of weeks in, I got a sore shin and returned to the UK, where I picked up a bad hamstring and that was the final nail in the coffin for my World Championship hopes.”
