Speaking on BBC WM, Kelly Osbourne said it was fitting for the airport to be named after her father, because “this city made him and he made this city”.
Supporters of the idea have pointed to airports in other cities around the world, named after famous figures, such as John Lennon airport in Liverpool, JFK and LaGuardia in New York and Louis Armstrong in New Orleans.
Mr Hudson said his campaign was going “pretty well” and he had received a “really good response” when he raised the issue at a recent Birmingham City Council meeting.
He said he also had the backing of most of Ozzy Osbourne’s family.
Birmingham Airport most recent statement on the issue said: “We are currently progressing an exciting homage to Ozzy Osbourne, creating a greater sense of place for Birmingham and his fans.
“We know he was an inspiration to so many in our region proving talent, hard work and commitment can take you to all corners of the world and we are committed to honouring his legacy within our terminal space.”