From Longman Dictionary of Contemporary EnglishI don’t suppose (that)I don’t suppose (that)a) used to ask a question in an indirect way, especially if you think the answer will be ‘no’ I don’t suppose you have any idea where my address book is, do you? b) ASK FOR something/ASK somebody TO DO somethingPOLITEused to ask for something in a very polite way I don’t suppose you’d give me a lift to the station? c) PROBABLY#used to say that you think it is unlikely something will happen I don’t suppose I’ll ever see her again. → suppose
Examples from the CorpusI don’t suppose (that)• I don't suppose the painting will ever be worth a thousand dollars.• I don't suppose you'd be willing to go get the napkins?• I don't suppose you have any idea where my address book is, do you?