The professional dancer was speaking during rehearsals for his sell-out solo tour when he made the confession.
Len Goodman retired as head judge at the end of last series, with a successor yet to be named.
Brendan told ITV News: “I’d like to think that the BBC would at least consider me for the role. I put my hat in the ring. I make no bones about it.
“But whoever they choose will be the right decision for the show.
Strictly Come Dancing: Brendan Cole said he would like to replace Len Goodman
Strictly Come Dancing: Brendan was speaking ahead of his sell-out solo tour
I put my hat in the ring
“I keep telling the audience my new catchphrase, which is “Bren’s-Lens”. I’m hoping it will catch on.”
Brendan has been on every series of Strictly Come Dancing since its beginning in 2004.
The 40-year-old has also served as a judge on Dancing With The Stars, New Zealand, where he's originally from.
Strictly Come Dancing: Gary Edwards is hot favourite to replace Len
Strictly Come Dancing live tour
Fri, January 20, 2017
Daisy Lowe and Louise Redknapp put their dancing shoes back on yesterday and dazzled in boob-baring dresses at the Strictly Come Dancing live tour photocall.
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The Strictly Come Dancing live tour
Despite Brendan’s impressive CV, last week Gary Edwards emerged as the frontrunner to fill the empty place on the judging panel.
Anton Du Beke, Karen Hardy, Arlene Phillips and Helen Richey have also been tipped as possibilities.
Strictly Come Dancing will return to BBC One later this year.