It was reported last week that ITV is in talks to revamp the classic game show, originally hosted by Roy Walker.
Britain's Got More Talent presenter Mulhern has now been approached to front the new series, according to The Sun.
"Stephen is over the moon that he is going to front the revival of such an iconic show," a source apparently told the tabloid.
"He feels he has worked his apprenticeship at ITV2 and has been rewarded with a fantastic opportunity. He can't wait to get started. He's really excited about it and has been watching old reruns."
Northern Irish television personality and comic Walker hosted the original Catchphrase between 1986 and 1999, followed by Nick Weir from 2000 to 2002 and finally Mark Curry in 2002.
> Stephen Mulhern's Britain's Got Talent blog
Watch a classic Catchphrase clip below:
Photo gallery - DS Icon Roy Walker: