The phrase "a message suggesting that" is correct and usable in written English.
It can be used when introducing a statement or idea that implies or hints at something without stating it directly.
Example: "The report included a message suggesting that further research is needed to validate the findings."
Alternatives: "a note indicating that" or "a communication implying that".
He later sent a message suggesting that his account had been hacked.
Yet he did so reluctantly, and an hour before the interview, he left a message suggesting that it be postponed.
One blogger advised readers to use baking soda to clean pet stains on carpets, while the mother who runs the Canning With Kids blog sent a message suggesting that readers "decorate with plants that clean the air".
Shortly after Ioffe's piece appeared, the Wall Street Journal's Byron Tau pointed out that on October 12, 2016, just fifteen minutes after WikiLeaks sent Trump, Jr., a message suggesting that his father should tweet out a link to a WikiLeaks search tool, Trump tweeted, "Very little pick-up by the dishonest media of incredible information provided by WikiLeaks.
Chris recalled having a woman send him a message suggesting that by living their lifestyle, the three were "ruining gay marriage for everybody".
My visit was pleasant, and I called and left a message suggesting that along with our husbands, we get together sometime soon.
He said the policy clearly indicated, without saying so explicitly, that what was expected was a religious message, "suggesting that a solemn, yet nonreligious, message, such as commentary on United States foreign policy, would be prohibited".
Early this month, Mr. Rogozin, the Russian deputy prime minister, posted a Twitter message suggesting that Romania had a secret plan to annex Moldova, after supporting Moldova's integration into Europe.
Persuading the Peloponnesians to join the Athenian fleet, Themistocles then lured Xerxes by a false message, suggesting that he himself was ready to change sides, into ordering an all-out attack.
The self-described "hash godfather," he officially invented the Twitter hashtag in August 2007, when he sent out a Twitter message suggesting that the pound symbol be used for organizing groups on Twitter.
And Doku Umarov, the Chechen guerrilla leader who claimed responsibility for the suicide bombings in the Moscow subway, took the same line in a videotaped message, suggesting that the real terrorist was his nemesis, Vladimir V. Putin, the Russian prime minister.
