The rap mogul's wife Beyonce gave birth to Blue Ivy in January and Osbourne is a month into parenthood with baby Pearl. Both men have been shortlisted for the Premier Inn Celebrity Dad of the Year prize.
Sir Elton John and N-Dubz rapper Dappy have also been tipped for the award, which 'Mysterious Girl' hitmaker Peter Andre was given last year.
"Take That" star Barlow, whose wife is pregnant with their fourth child, is ecstatic about the title.