The club recently secured defensive trio Michael Smith, Christophe Berra and John Souttar on new deals.
Last week Levein revealed that contract offers would also be made to players seen as key to pushing the team forward on the pitch.
Naismith, the team’s top scorer on 13 goals in all competitions, is currently on loan from Norwich City. He is out of contract at the end of the season and free to speak to clubs.
Meanwhile, Djoum’s current deal expires at the end of May. Levein had concerns about being able to keep the Cameroonian, who has been one of Hearts’ most influential players in recent weeks. However an offer has been put ot the 29-year-old.
“I’m trying,” he said. “My strike rate isn’t bad so far, so I’ll just need to keep it going.
“It would be good to get all the ones signed up who give us that stability I keep talking about. I’ll just wait and see what happens.
“I want Arnaud to stay but he said to me a while ago that if something comes up that at his age is worth an awful lot of money, then he would probably look to take it.
“But I’ll keep chipping away. He likes it here in Edinburgh and his family are settled. There is more to life than money.
“I believe Steven is happy here but again it depends on whether something else comes up in the next couple of months that piques his interest.
“But I’ll keep plugging away.”
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