From Longman Dictionary of Contemporary Englishhave a vague idea/feeling/recollection etc (that)have a vague idea/feeling/recollection etc (that)THINK SO/NOT BE SUREto think that something might be true or that you remember something, although you cannot be sure Larry had the vague feeling he’d done something embarrassing the night before. → vague
Examples from the Corpus
have a vague idea/feeling/recollection etc (that)• I can remember nothing of them, but I have a vague feeling of having been well cared for. 