"After lengthy discussions with Martin O'Neill, Ian McLeod and Jim Hone, I've agreed to stay at Celtic in order to continue with the work I've only recently begun.
"It's important to me that the base at this club is strong, and that's what
I see my job being all about.
"It's important for me to get that right because I want Celtic developing
the very best young players.
"I've already tuned myself into that job and, with the board and the manager
showing their faith in my ability to achieve that, I felt it was only right
that I showed the same commitment to them.
"If I had gone to Kilmarnock, it would have been done only to further
myself, and that's not what I want at this stage.
"I've no doubt that I would like to return to the crazy world of football
management at some point but, at the moment, I'm happy to dedicate my future to ensuring that Celtic Football Club establishes the best possible youth
set-up.
"I had four-and-a-half very happy years at Rugby Park both as a player and a
manager, and I was certainly very flattered that they thought enough of me
to ask me to return.
"But I'm less than three months into my job here at Celtic Park, and I don't
want to leave the whole process to be started up again."
Burns had also been hinted at as the new assistant to Berti Vogts in the Scotland set - up but no moves have been made there yet and there has certainly been no official approach from ther SFA to Celtic for Burns' services.
Earlier in the season Burns had shown an interest in taking the vacant St Johnstone manager post but in the end his former assistant at Parkhead, Billy Stark, was installed at McDermott Park.
Celtic Manager Martin O'Neill was said to be delighted that Burns had decided to remain in his current post.