To insinuate something (especially something bad or insulting) is to say it in a subtle or indirect way. Insinuate can also mean "to gradually make (oneself) a part of a group, a person's life, etc., often by behaving in a dishonest way."

// When the teacher questioned the students about their identical test answers, they knew she was insinuating that they had cheated.

// They have managed to insinuate themselves into the city's most influential social circles.

See the entry >

"... when perennial talk among beachgoers about where to spend those beautiful but fleeting summer days involves rumors that, perhaps Narragansett is, say, uninviting to nonlocals, officials contend that just isn't true. 'When people say that or insinuate that Narragansett Town Beach is unfriendly or unwelcoming to nonresidents, this is absolutely untruthful,' said Parks and Recreation director Michelle Kershaw." — Christopher Gavin, The Boston Globe, 3 Nov. 2024

Insinuating involves a kind of figurative bending or curving around your meaning: you introduce something—an idea, an accusation, a point of view—without saying it directly. The winding path is visible in the word’s etymology: insinuate comes from the Latin verb sinuare, meaning "to bend or curve," which in turn comes from the Latin noun sinus, meaning "curve." The influence of Latin sinus is visible elsewhere too: in the mathematical terms sine and cosine, the adjective sinuous ("having many twists and turns"), and the noun sinus ("any of several spaces in the skull that connect with the nostrils").