The most common and most likely answer to this crossword clue is the 4 plus 5 letter word PIPE DREAM
I've seen this crossword clue in The Daily Telegraph
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More clues leading to the result PIPE DREAM
- Fanciful scheme for the Tube?
- Fanciful plan of Dickens’ protagonist formed on reflection to capture Fred’s heart
- Spot journalist and paper giving false hope
- Unrealistic idea associated with churchwarden?
- Fanciful hope conveyed about a male
- Fanciful plan to narrowly beat editor on paper
- Disgust over senior journalist on papers showing fanciful ambition
- I, pampered at sea? A fanciful hope
- Churchwarden eg somehow made vicar, finally – sheer fancy!
- Fancy whistle — end of time in short
Buddy explains!

The straight part
We know that "Fantastic notion" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case fantastic notion = pipe dream.The cryptic/wordplay part
In cryptic crossword there's often an wordplay/cryptic part as well.This part involves a more complex hint, such as an anagram, homophone, hidden word, etc.
Sadly, We don't have an explanation for this specific crossword clue yet.