The defender’s current deal expires at the end of the season.
Evans is preparing for Thursday’s Europa League opener with Zorya Luhansk and is open to penning fresh terms at the King Power Stadium.
He said: “There’s been nothing formal in terms of contract talks, possibly that’s something my agent and the club will do in the near future, but I have really enjoyed my time here, if that option becomes available I’m sure it’s one I would take.
“If we can come to an agreement I’m sure it won’t be a problem and it will be sorted soon.”
The 32-year-old joined from West Brom for £3.5million after the Baggies’ relegation in 2018 and has made 77 appearances for the Foxes, scoring three goals.
He helped them to fifth in the Premier League last season and believes they need to embrace the Europa League, where they also face Braga and AEK Athens in Group G.
He said: “It’s very important (to start well), it’s a home game and we’re stepping into the unknown a little because they (Zorya) have played in the Europa League more and have a bit more experience.
“We know it will be a tough group to get out of but we’re confident, especially if we get off to a good start.
“Travelling around Europe with your team-mates and going to the different stadiums, you never get that back. They are great occasions, we have been looking forward to it and I’m sure we’ll relish it.”
Jamie Vardy remains out with a calf issue, Wilfred Ndidi is sidelined with a hip injury, Caglar Soyuncu suffered a serious abductor injury on international duty with Turkey while Ricardo Pereira is a long-term absentee with an Achilles injury.
Islam Slimani is unavailable having been left out of the Foxes’ European squad.
Boss Brendan Rodgers said: “The squad had to be handed in much earlier than the Premier League squad and unfortunately, thinking maybe he (Slimani) wasn’t going to be here, that’s the reason why.
“We just have to find ways to be more creative and more clinical. We have to work with the players we have, we go into each game with the confidence to create and score goals and it will be no different on Thursday.
“The idea is to get out (of the group) and qualify. Then you look to progress from that. You don’t want to look too far ahead, it’s a great competition to be in and an experience for the players who haven’t sampled European football before.
“It develops you as a player, tactically, physically and mentally.”
