Manager Neil Lennon revealed at the Easter Road side’s recent annual meeting that stalwart Stevenson would be offered fresh terms ahead of his current deal expiring next summer.
The full-back, who was awarded a testimonial against Sunderland last year to recognise a dozen years of service at Hibs, is thrilled at the prospect of another extension at the club where he is the only player ever to have won two cups.
The 30-year-old, who made his Scotland debut against Peru in the summer, has set his sights on still being at Hibs when he eventually hangs up his boots.
He said: “The club have told me I will be offered a new contract and I’m delighted about it. I just want to get it signed and focus on my football. As a footballer, it gives you peace of mind to know that you are wanted and the club value your contribution.
“Hopefully, I have several years to go before I end my playing career, but I would love to finish it here at Hibs.
“I know what football is like, I’ve seen so many people come and go, and if I want to be here for the long term, then I need to earn it.
“Right now, I feel as fit and as healthy as I did when I was 19.”
Stevenson, who made his Hibs debut as a 16-year-old in 2005, created history when he lifted the Scottish Cup two years ago.
Having also been instrumental as the Easter Road side scooped the CIS Cup in 2007, the Fifer has achieved something even the club’s Famous Five heroes never managed.