The Cameroon midfielder, who signed for the Capital outfit in September 2015 following a spell at Lech Poznan in Poland, is out of contract at the end of this season.
The 29-year-old returned to the first team in September after battling back from a ruptured Achilles suffered last February and has started Hearts’ last nine matches.
Despite previously appearing keen on a move to the French football, Djoum – an Africa Cup of Nations winner with Cameroon in 2017 – has revealed his desire to sign a new deal at Tynecastle.
Speaking in the French media, he said: “I like it here. This is my fourth season.
“Edinburgh is a beautiful city. My family are well, my wife and two children.
“This city is a bit special for us. I would like to stay at Hearts.
“The people around the club are really nice – they take good care of me.
“I’d like to sign up for the duration here.”