Scandal against Queen Elizabeth

The following note occurs in vol. iv. p. 135. of Burton's *Parliamentary Diary*:— "Osborn,—see his works (1673), p. 442,—says, 'Queen Elizabeth had a son, bred in the state of Venice, and a daughter, I know not where or when;' with other strange tales that went on her I neglect to insert, as fitter for a romance than to mingle with so much truth and integrity as I profess." Is this rumour any where else alluded to? and if so, upon what foundation?