The phrase "a statement suggesting that" is correct and usable in written English.
It can be used when introducing a claim or assertion that implies a particular idea or conclusion.
Example: "The report includes a statement suggesting that further research is needed to validate the findings."
Alternatives: "a claim indicating that" or "an assertion proposing that".
Well, a Samsung spokesperson just sent me a statement suggesting that wasn't the case.
Later, the interior ministry released a statement suggesting that some of them had faked their injuries.
On Friday, however, Greenberg issued a statement suggesting that a merger deal was unlikely.
After the interview, the United Nations released a statement suggesting that the interview had been highly informative.
Several hours after the Mayor's news conference, Tishman released a statement suggesting that there had been a misunderstanding.
After the riots, the Kurdish Democratic Party in Iraq issued a statement suggesting that Damascus do something to end the problems in "Syrian Kurdistan" peacefully.
The fact that the normally buttoned-up special counsel's office felt compelled to issue a statement suggests that the story's conclusions were too baldly stated and too consequential to stay unchallenged.
Hours later, the two oligarchs issued a conciliatory statement, suggesting that, for now, the heat was off Mr Deripaska.
Yesterday, Dr. Fulani released a written statement suggesting that her comments could be used to improve communication among different groups in the city.
Gergely Gulyas, the parliamentary leader of Mr. Orban's party, released a brief statement suggesting that the council's work was free of political interference.
Three judges, however, issued a dissenting statement suggesting that vote swapping is illegal vote buying not protected by the First Amendment, and it is quite possible that another court would agree with the dissenters should the issue arise again.
