the German's form and antagonising the fickle Paris crowd.
On the only occasion the two men have played, in Monte Carlo four years ago, Murray won just three games and was jeered off by a section of the fans. Given the Parisians' liking for a bit of barracking, deserved or not, Murray will be keen to keep them quiet by outplaying the German.
Kohlschreiber, 30, won the title in Duesseldorf at the weekend, lifting his ranking to No.24, and Murray knows he is likely to be in for a bit of a dogfight against a man who knows his way around a clay court.
"He's a quality player," said Murray, who has dropped just one set in two matches so far. "He's had big results here before, beating Novak [Djokovic, in 2009], and won last week so he's bound to be confident.
"It's going to be a very tough match for me so I'll need to play very well to beat him because, when I played him before [in Monte Carlo], when I didn't play well, it was a pretty quick win for him."
Murray is a popular player with fans around the world but the French crowd are notorious for turning on players whom they don't think are giving 100% or, sometimes, if they are not good enough. Keeping them quiet will be on Murray's mind as he tries to seal a place in the last 16.
"[In] the first couple of matches, the crowd's been pretty full but, when the match isn't that close, it can be quite subdued," he said. "It just depends on the way the match is going and whether or not you can get the crowd into the match and feed off them a little bit."
Another day and more questions about the identity of Murray's new coach but, though the Scot has said he won't speak to potential candidates until after the French Open, he did explain that gender was not important, in itself.
"There are some men that will completely panic when something bad is happening in a match and there will be some women that will panic during matches," he said. "The ones that make the good coaches are the ones that are able to stay calm in those moments and can give sound, clear advice in pressure situations. When you've been there and done it, it's obviously easier to pass on that sort of advice."
Novak Djokovic and Roger Federer both dropped their first sets of the tournament but advanced to the last 16 with relative ease.
Second seed Djokovic, the bookmakers' favourite for the title despite the presence of eight-time champion Rafa Nadal, ousted the Croat Marin Cilic 6-3, 6-2, 6-7, 6-4. The Serb came from a break down to win the first set, coasted through the second and, after dropping the third, won the match when Cilic double-faulted.
"I felt great," said Djokovic, who now plays Jo-Wilfried Tsonga of France. "I had chances to get it done in straight sets but he started to play better. In the important moments I held my nerves."
Federer, the fourth seed and champion in 2009, dropped the second set to Dmitry Tursunov of Russia before winning 7-5, 6-7, 6-2, 6-4 to become the first man to reach the last 16 in Paris 12 times.
At 32, Federer is by far the eldest of the so-called big four but having made it through to the second week, the Swiss said he was feeling confident. "I know what are my assets, what are my weaknesses," he said. "Serve, return, that's quite okay. I've spent more than five or six hours on court, so I've got the information. I hope that I will step it up."
Next up for Federer is Ernests Gulbis, who beat him on clay in Rome in 2010 and who eased past the Czech veteran Radek Stepanek yesterday, 6-3, 6-2, 7-5. Since the retirement of Marat Safin, there is nothing quite like a Gulbis press conference and the Latvian was in full Edith Piaf mode as he claimed there was nothing about his career he would change.
Gulbis admitted that he made some bad decisions as a younger man. Having reached the quarter-finals in Paris aged 19, he went awol for several years as his off-court liking for fun outweighed his on-court work ethic.
Yet, he said it all made him appreciate his success more, only to then alienate half of the population when he said he would not want his two sisters to play professional tennis because "for a woman it's tough".
"A woman needs to enjoy life a bit more," he said, "needs to think about family, think about kids. [How] can you think about kids until you're 27 if you're a tennis player?"
The Twitter reaction was soon flying but Gulbis was more concerned with his match with Federer and the 25-year-old was confident he would have a good chance.
"I have a game plan. I know how I'm going to play him. You don't need to be scared to do certain things against him. Most people go on court and lose the match already before it's started. I can tell you that's not going to be the case with me."
John Isner became the first American to reach round four since Robby Ginepri in 2010, beating Spain's Tommy Robredo in four sets.