Micky Doherty says the two teams were not interested in the Irishman.
The Republic of Ireland international cost Everton just £60,000 when they snapped him up from Sligo Rovers in January 2009.
He went on to star in a loan spell at Blackpool before becoming the number one right-back for Everton in 2010.
But he could have gone elsewhere, as revealed by the man who spotted him today.
Micky Doherty was watching his son play for Sligo when he saw the then 21-year-old Coleman in action. Soon after he was appointed as an Everton scout and immediately told David Moyes to sign him.
But as he revealed today Burnley and Celtic must now be kicking themselves.
“When I saw Seamus play I was like ‘bloody hell he’s a talent’.
“He was fast, strong and had a great work ethic up and down the line.
“When I got the job at Everton, I put Seamus’ name to David Moyes and his staff.
"Everton decided to take him and came up with the £60,000 which was a no brainer because you would have got that money back.
“Paul Cook, manager of Sligo at the time, is a friend of mine and he told me that Seamus had gone over to Burnley and Celtic but they had turned their noses up at him.
“We started to show interest and other clubs began to think they had made a mistake.”
This of course comes in the week Coleman is set to make his 200th appearance for the club and, as reported by TMW earlier today, interest from Chelsea, where Doherty is now a chief scout, is now becoming very real.
Celtic have a rich history of talented Irish players and Coleman would have been an absolute star in the Scottish Premiership.
Meanwhile Burnley live for such bargains and both teams must wish they made a different decision on the Everton star.
Hindsight however is a beautiful thing and, as far as Everton are concerned, a futile endeavour, for a player who the Daily Star recently reported Everton would not sell for £50 million.