The performer, who has appeared on every series of Strictly, already has experience having previously appeared as a judge on the New Zealand version of the show, Dancing with the Stars.
"I would love to be a judge," Brendan told BBC Radio 2 this week. "I've told the BBC I'm up for the job if they would like to even consider me.
"Make no bones about it, it would be a great gig - it's a phenomenal slot."
However Brendan admitted he wasn't too sure on getting the job, saying: "They will probably have somebody else in mind".
Meanwhile, speaking to ITV news, Brendan admitted: "I'd like to think that the BBC would at least consider me for the role.
"I've put my hat in the ring. I make no bones about it. But whoever they choose will be the right decision for the show."
As yet the BBC has not confirmed any news about Len's replacement, but Strictly host Tess Daly spilled we should know by the Spring.
Speaking at the National Television Awards last month, Tess said: "We don't know [who it is] - it's still under discussion."
She added: "I'd imagine we'll know by April."
As well as Brendan, other pros Anton Du Beke and Karen Hardy have been rumoured for the role.
Strictly Come Dancing will be back on TV in the autumn.