It is believed that producers are keen to sign an A-List name to replace Sir Tom Jones on the coaching panel and had identified Lennox as their number one target.
However, as a spokesperson told The Mirror, the former Eurythmics star has criticised talent shows in the past and is not prepared to endorse any in the future.
“Annie has been vocal in the past about her distaste for talent shows so it would have been somewhat hypocritical to take part,” the source told the paper.
The paper goes on to state that Lulu may be next in line for the position on the panel.
It was reported earlier this month that Jessie J has quit the show whilst Sir Tom Jones was undecided on his future.
Meanwhile, Annie Lennox took part in the closing ceremony for thr Olympic Games this past weekend.
Photos: Annie Lennox and more at the Olympic Games closing ceremony