The Championship side have been keeping an eye on the pair according to the Scottish Sun, and they were watched during Hearts’ 2-1 win against Kilmarnock at Rugby Park earlier this month, a game in which Naismith scored.
Birmingham, who sit eighth in the English second tier, have financial restraints meaning manager Garry Monk has to operate in the free agent market.
Both Djoum and Naismith are out of contract at the end of the season and therefore free to speak to interested clubs.
As Craig Levein confirmed, Hearts have offered deals to the duo but the players are keen to assess all options available to them.
“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.”
They have been influential to Hearts’ season so far. Following injury problems Djoum has emerged as one of the team’s best players in recent weeks, while Naismith is the top scorer on 13 goals despite missing a chunk of the campaign.
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