suggest itself to

suggest itself to (one)

Of an idea, to come into one's mind seemingly out of nowhere. A plan to take over the company suggested itself to Samantha. An exciting new idea suggested itself to me while I was listening to the speaker give his presentation.
See also: itself, suggest
Farlex Dictionary of Idioms. © 2015 Farlex, Inc, all rights reserved.

suggest itself to someone

[for an idea] to seem to present itself to someone. A new scheme suggested itself to Alice as she looked at the records of the last attempt. As you read this, does anything suggest itself to you?
See also: itself, suggest
McGraw-Hill Dictionary of American Idioms and Phrasal Verbs. © 2002 by The McGraw-Hill Companies, Inc.
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References in classic literature ?
The third and most incomprehensible thing is that people studying history deliberately avoid seeing that this flank march cannot be attributed to any one man, that no one ever foresaw it, and that in reality, like the retreat from Fili, it did not suggest itself to anyone in its entirety, but resulted- moment by moment, step by step, event by event- from an endless number of most diverse circumstances and was only seen in its entirety when it had been accomplished and belonged to the past.
SIMPLE as it may seem when once thought out, the common method of indexing maps by a conventional system of co-ordinates defining the positions of places upon them did not, it seems, suggest itself to geographers until some time after the printing of maps had come into vogue.
Suicide is a crime the most revolting to the feelings; nor does any reason suggest itself to our understanding by which it can be justified.
But in the cold light of day one option does suggest itself to be the most favourable and that involves the expansion of existing facilities, whether these are at Coventry or Birmingham.
The solution is not entirely convincing, but what is convincing is that Kornexl has taken everything into consideration and nothing better suggests itself to her, and is, therefore, unlikely to suggest itself to anyone else.