Fiorentina winger Juan Cuadrado has made it clear he wants to join Chelsea, Sky sources understand.
Manager Sam Allardyce admits he is unsure whether Darren Fletcher will choose to join West Ham or another club.
A graduate of the Hibs academy, the 25-year-old made his first-team debut in 2005 and has since recorded 172 appearances - winning last season's player of the year award.
Stevenson, the club's longest-serving player, said: "I'm really pleased to have agreed another contract with Hibs - this is a special club and I feel privileged to be a part of it.
"If somebody had told me when I first joined Hibs as a 14-year-old that I would still be at the club 11 years later then I wouldn't have believed them.
"Hibs have played a big part in my life over the years - it's my club - and I'm really excited about the future and what we are building here."
This season Stevenson has been utilised in centre midfield, left-back and right-back but he stressed that he is always willing to put the needs of the team first.
He added: "I'm happy to play wherever the manager decides I should play - I will always give my all for Hibs, although I've yet to play in goals or up front."
Manager Pat Fenlon believes the player has a key role to play in the continued development of the club.
He said: "Lewis has a fantastic attitude and he always works incredibly hard for the team - he is a good professional.
"We are building a club here and one of the key factors behind making that become a reality is continuity, which means retaining important players.
"Ever since I joined the club, Lewis has been great and never sells himself short. He always gives everything for the shirt and I'm delighted to have him on board for the next two years."