The Scot was kept off the grass of Wimbledon's Aorangi Park practice courts by heavy rain and instead hit on the indoor hard courts with British number three James Ward.
He would hope to get back on the grass on Sunday before taking on 6ft 8in Anderson in the last 16 the following day.
Murray has won his last 16 singles matches at the All England Club, first winning Olympic gold in 2012 and then adding the big one last summer.
His 16th victory was one of his most impressive in many ways, Murray making world number 23 Roberto Bautista Agut look like a novice on grass - the Spaniard won a title on the surface last week.
"It's been good," said Murray of his week. "I played well from the first game of the first match pretty much through until the end of the last one. I haven't used up too much energy."
It has been the third seed's most decisive first week at the All England Club, Murray spending just over five hours on court in his three matches and losing only 19 games.
He has been determined to be ruthless to give himself the best possible chance of retaining his title.
"You can lose a slam in the first week by playing three five-set matches or two five-set matches," he said. "They do take their toll a little bit.
"I obviously have a couple days off now as well, so I'll be able to work on a couple of things on the practice court, then get ready for Monday."
That Murray is feeling good physically is particularly good news given it is only nine months since he underwent back surgery.
It has been a lengthy and at times frustrating road back, with Murray not having won a title or reached a final since Wimbledon last year.
But over the last month and a half he has rediscovered his best form, and he said: "I'd say I'm happy with where my body's at right now.
"Physically I feel good. My back feels much better than it did at this stage last year, so that's a big positive for me.
"I've spoken to a few people that have had surgeries, ex-players and stuff. They said it was six to nine months from when they started playing again until they actually started to feel their best."
It was obvious at the French Open that Murray had not regained all of his physical stamina and he was soundly beaten by Rafael Nadal in the semi-finals.
In the earlier rounds he had often allowed commanding positions to slip away and become frustrated and agitated, but at Wimbledon so far he has been a picture of calm authority.
"I'm in familiar surroundings," he said. "That's going to make you feel more comfortable. Just being at home, staying in your own bed, having all of your friends and family around you, you're going to feel more relaxed away from the court.
"The nerves and the pressure here is also different to other tournaments for me. It's probably greater here than it is at the other grand slams.
"But I enjoy pressure. I like feeling nervous. I'm not scared of that feeling. I've felt like I played my best tennis when I've been under pressure. I obviously love playing here."
It would be a surprise if Murray is not troubled more in his next match, with Anderson's serve making him a real danger on grass in particular.
The 28-year-old South African, who is through to the fourth round for the first time, is having the best season of his career and is at a high of 18th in the rankings.
Anderson's only previous match on a grand slam centre court came against Murray on Rod Laver Arena at the Australian Open in 2010, when he won just four games.
He did beat the Scot a year later in Canada and is looking forward to taking on the home favourite on his stage.
Anderson struggled with a stiff back in his third-round win over Fabio Fognini, partly as a result of nerves, but is confident that will not be a problem on Monday.
He said: "It will be a great experience for me. It's why I play this game, to play greats, and at such a big tournament.
"There will be a few challenges. I think the biggest will be staying calm, regardless of what court we may be on or all those outside factors.
"Really it's about me focusing on my game. If I do that and do it very well, then I might have a few chances here and there."
There was also a bonus on Friday for Anderson when he met comedian Ricky Gervais, who was at Wimbledon to support Murray.
"I went and introduced myself," said Anderson. "It was great. I was a little nervous. My hand started sweating. When you're not used to something it's amazing what you get nervous about."