The Algeria forward told the Foxes he wants to leave after an underwhelming follow-up season to their title-winning campaign in 2015/16.
He has not handed in an official transfer request, but said earlier in the summer it was "time to move on" and that he had a gentleman's agreement with the club to do so.
The 26-year-old is currently in Hong Kong taking part in the Asia Trophy with City and, speaking to Sky Sports from the competition, Shakespeare said: "I think I was quoted on the last press day that there was no bids.
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"There was a bid from Roma I was told afterwards, so I would like to put the record straight on that one.
"It was politely declined on the basis that it was a low offer. Of what that offer is, don't ask me how much because I don't know and I don't get involved in that."
Roma are on the lookout for a new forward after the departure of Mohamed Salah to Liverpool.
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