Evans has been on the books of Leicester since the summer of 2018 when he joined from West Bromwich Albion for 3.5 million pounds.
The 32-year-old defender has established himself as an important player in the Foxes team.
The Northern Ireland international made 21 starts and three substitute appearances in the Premier League for Leicester during the 2018-19 season, scoring one goal in the process.
The former Manchester United defender played in all 38 games for the Foxes last season, scoring one goal and providing one assist in the process.
Evans has played thrice in the Premier League for Leicester so far this season, and he has said that he would like to stay at the King Power Stadium beyond next summer when his current contract runs out.
The defender told Sky Sports: “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.”