To imply is to indicate without actual statement something that is to be inferred (See imply, infer). TO insinuate is to hint slyly or subtly, to instill an idea by tricky, subtle, or underhanded means. Insinuate also means "to enter or introduce by devious ways." "Sis insinuated herself into the group over the protests of some members." "This is propaganda insinuated into the unsuspecting minds of citizens." "Did the speaker intend to imply that we have insinuated in people's minds doubt about the real purpose of his actions?"
Dictionary of problem words and expressions. Harry Shaw. 1975.