The midfield pair are expected to rejoin the squad at Riccarton after Achilles and calf injuries respectively.
Djoum has not played since February after snapping an Achilles tendon, whilst Cowie received an injection for a calf strain earlier this month. They have not featured in any pre-season friendlies but are now on the verge of taking a hugely positive step in their recovery.
“Arnaud has been out with his Achilles problem but he is getting close to coming back. Don is getting close to coming back as well,” said Craig Levein, the Hearts manager.
“He strained his calf in pre-season and got an injection. He’s had a period of rest and now he’s building himself back up again.
“We should see them ready to join in full training at some point in the next week to ten days.”
Medical staff initially predicted an eight-month absence for Djoum but he is slightly ahead of schedule having started running again last month. He is not expected to be ready to play for several weeks yet.
“Arnaud will obviously have to do a fair period of training to get himself up to speed, but I expect to see him make a start in the next week to ten days,” added Levein. “Don hasn’t done anything in terms of matches in pre-season but he’s experienced. I don’t normally worry too much about the senior guys. They can generally get into the game and certainly not have a disaster, even if they are a bit rusty.”