The former England captain, who has moved back to his native Suffolk, has also cast doubt on returning to Scotland to work again.
Hibs announced on 10 June, just a fortnight after they were relegated to the Championship following a two-legged play-off defeat by Hamilton, that they had “relieved” the former England captain “of his duties”.
Since then, former Celtic defender Alan Stubbs has been appointed as the club’s head coach.
Hibs brought Butcher, along with his assistant Maurice Malpas, to Hibs from Inverness in November 2013 on a three-year deal.
It is understood the 55-year-old, who has been linked with the vacant New Zealand manager’s role, and Malpas are still being paid by Hibs according to the agreement of their respective contracts.
And should Hibs attempt officially to sever all ties with the pair, the club would have to reach a severance deal for the remainder of their deals.
Speaking for the first time since departing the club, Butcher, who had relocated from Inverness to North Berwick after moving to Hibs, told Radio 5 live: “I don’t regret it [taking on the job] at all.
“I’m on gardening leave just now, the garden is magnificent and I shall be in the Chelsea flower show next year, I’m looking forward to that.
“I’ve been doing the garden, I’ve been enjoying the Suffolk air, I met George Burley – one of my colleagues at Ipswich – and he is not working too.
“We’ll probably set up an ex-managers club somewhere and set up shop there. I live in Suffolk, my wife’s parents and my own parents are doing very well. I’ll go and watch Ipswich play, I’ll probably become a season ticket holder. I’ve always wanted to do that.”
New chief executive Leeann Dempster’s recommendation to remove Butcher and Malpas was rubber-stamped by the Hibs board after the pair presided over a disastrous run of form that led to the team’s relegation from the Premiership.
Butcher first became a manager in Scotland with Motherwell in 2002 before leaving in 2006 for spells at Sydney and Brentford.
He moved to Inverness in 2009 before taking up the post at Easter Road.
But Butcher reckons it is unlikely he will return north of the border. He added: “I’ve done my time up there, I’ve done a lot of time up there; I think my visa finally ran out.
“I miss football to a certain degree but it’s nice to look forward to a season without having any real pressure.
“It’s nice to have a look round, go to some clubs. I’ve spoken to some lovely people within the game who have said, ‘come along and come and see us train’.”
Despite being a passionate Englishman and captaining his country at the World Cup finals, Butcher also had a spell on the Scotland management team when he was an assistant to Burley in 2008 and worked alongside his former Ipswich Town team-mate on the failed 2010 World Cup qualifying campaign.
In November 2009, Burley was sacked as Scotland manager and, at the same time, Butcher left by mutual consent.