Martinez was appointed the manager of Wigan manager in June 2009 when the Latics were in the Premier League.
The 45-year-old Spanish defensive midfielder played for the Latics from 1995 until 2001.
The former Swansea City and Everton manager has revealed that he was approached by Celtic in 2009 before he took the Wigan job.
Martinez told The Evening Times: “I had conversations and I was always very impressed with the need to bring silverware. There was also the prospect of getting to the Champions League through the qualifying rounds and it was always a club that people are attracted to because of the intensity of the fans and what it means. “
“But at that time I had to go back to where I started my career in the UK and where I started my coaching career at Wigan.
"In life there has to be the right timing for moves and at that time I wasn’t prepared to go away from my beginnings in the UK.
“It was a chance to go and work again with Dave Whelan - the man who had brought me to Britain.”
Managers at Celtic
Celtic appoints Tony Mowbray as their manager in the summer of 2009, but he could last only until March 2010.
Neil Lennon replaced Mowbray, and under him Celtic dominated Scottish football for the next few years before he stepped down for Ronny Deila to take over in June 2014.
As for Martinez, after achieving considerable amount of success with Wigan, the Spaniard was appointed the Everton boss in 2013, and in 2016 he took charge of the Belgium national football team, who did remarkably well at the 2018 World Cup in Russia in the summer.