Roberto Martinez asked to leave Wigan Athletic on Tuesday having guided the club to FA Cup glory days before being relegated from the Premier League, with Everton and Stoke City already linked with his signature.
The Spaniard had been in charge since 2009, having previously helped turn Swansea City into one of Britain's most attractive sides.
Wigan pulled off a series of relegation escapes under Martinez while winning admirers for their attacking football and he turned down an approach from Aston Villa two years ago.
The underdogs then managed a 1-0 FA Cup final triumph over Manchester City earlier this month to win their first major trophy but were relegated three days later after eight years in the top flight.
"He wanted permission to move so I've given that. He has 12 months left on his contract, so whoever comes in for him must pay the remainder of his contract," Wigan owner Dave Whelan told the BBC.
"He feels he's not the man to lead us into the Premier League. I've got to accept what he feels. He loves Wigan and the fans. We have to move on now and want applications for the job."
Former Wigan midfielder Martinez, who made his name as a player in the English lower divisions rather than Spain, could also be a target in his homeland.
Martinez recruited heavily from Central America during his time at Wigan on a relatively limited budget but was criticised by fans for not shoring up a leaky defence.