Murray holds a 6-3 edge over the giant Argentine, notably downing Del Potro in a gruelling Olympic final to claim a second straight singles gold medal in Rio.
But Del Potro avenged that defeat as he rallied from behind to overcome Murray in a five-set epic in last year's Davis Cup semi-finals, with Argentina going on to secure their maiden title.
Their third-round clash at Roland Garros represents just the second time the pair have met at a Grand Slam, Murray winning their only previous encounter at the 2008 US Open.
"It's a tough match. Not an easy third round. He's, in my opinion, one of the best players in the world when he's fit and healthy," Murray said of Del Potro.
"This year he's had a lot of tough draws. If you look at the matches that he's lost, I think he's played Novak (Djokovic) a few times. I think he lost to (Milos) Raonic in Delray Beach.
"Miami I think he lost to Roger (Federer). So because of the ranking that he has, he's kind of in that bracket where he's met a lot of the top guys early on."
Murray suffered a shock fourth-round exit at the Australian Open and his struggle for form was further highlighted by premature exits at Monte Carlo, Madrid and Rome in the build-up to Paris.
But the Scot, who reached the final at Roland Garros for the first time a year ago, feels his level is improving.
"I definitely feel like I'm capable of winning that match. I mean, I'm playing way better than I was two weeks ago," said Murray who beat Martin Klizan in the second round on Thursday.
"(Thursday's) match will have done me a lot of good, because physically I pulled up well and felt good, so I will gain a lot of confidence from that."
Del Potro, who is making his French Open comeback after a five-year absence, thrashed Guido Pella in his opener before advancing to the last 32 when Nicolas Almagro succumbed to a knee injury.
The 28-year-old was hailed for his sportsmanship as he embraced and consoled the sobbing, stricken Spaniard courtside.
But the 29th seed, whose loss to Gastao Elias in Lyon last week was his only defeat this season to a player outside the top 10, knows he must quickly re-focus for his showdown with Murray.
"Last year we waged fiercely contested battles. So the stakes are high. I will have to fight again, but we are on a par," said Del Potro.
"I won't be the favourite, but when you are playing against these great champions, it's an opportunity to enjoy the moment and play well."