Representatives of the All England Club have discreetly told some of the game's worst offenders to keep the noise to a minimum.
The move comes after Portuguese teenager Michelle Larcher de Brito was warned over her loud and lengthy wails while playing her shots at last month's French Open.
The 16-year-old, who has a wildcard entry to Wimbledon, was booed off court in Paris.
An un-named source from the All England club told the Daily Express on Monday: "People have had a discreet word with de Britos' camp. If it continues on court, she will get a warning. Other people have been spoken to as well."
International Tennis Federation grand slam director Bill Babcock said the persistence of de Brito's grunts were of particular concern because they could distract other players.
"The noise extends into the hitting preparation time of her opponent, and that creates problems," he said.
Former French Open champion Sue Barker, now the face of the BBC's tennis coverage, believes the shriekers are damaging the sport.
"I have lost count of the number of people who have written to me saying grunting spoils their enjoyment of a match," Barker told The Sunday Times.
"It's unattractive, it's distracting.
"I would like to see it ultimately done away with. But while they should tighten up the rules, you cannot expect a player to stop immediately."
Russian star Maria Sharapova and former great Monica Seles have come under fire in the past for their vocal styles of play.
