Mallett said he was satisfied with the 24-16 victory over Australia on Saturday, but said White needed to blood some youngsters in the next tour with a view to next year's World Cup.
"Regarding the European tour, I'd like to see some rugby people and some medical people get together with SA Rugby administrators and suggest that five or six key players go into rehab or have a rest or whatever," Mallett said.
"They should be allowed to finish up and have a decent break.
"I think that what is in SA's best interests is to take some young form players in the Currie Cup to Europe and see how they perform.
"Let Jake White not be judged solely on results and let's see how the younger players shape up while some veterans are rested ahead of the World Cup.
"Some very good Currie Cup rugby has been played this season and if Pierre Spies, who wasn't much talked about at the beginning of the season, can make such a tremendous impression, why can't some others?
"Robbie Diack clearly has something. It wouldn't do any harm to take Luke Watson, and perhaps he and Jake would find there isn't such a gulf between them.
"There's a real raft of young talent at the Sharks - including Francois Steyn and Bradley Barritt. All Black Dan Carter was thrown in at a similar age.
"I don't want to keep mentioning names, but I think we would be well served by taking some youngsters along."
South Africa face England twice and France on their end of year tour.