Aston Villa left-back has been out of action since November.
Amavi was a summer signing from French side Nice and quickly became a fan favourite, only to suffer a cruciate knee ligament injury.
The Frenchman picked up the injury on duty with France's under-21 side back in November, with his absence a damaging one for the relegated side.
Black is positive about Amavi's progress, stating: "Jordan is progressing well. Obviously we won't see him again this season. He will need a full pre-season.
"He's done well but he's still got a lot of rehab work to do. It's not easy, it's a difficult injury. But we're pleased with how he's getting on.
"Jordan has started his career very well. He's a quality footballer - no doubt about it. Hopefully he will be ready to go next season."
The club website confirms Amavi is up and running again, and that being back to full fitness in time for the start of 2016/17 is the goal, and the fact Black hopes he will be ready for pre-season is a positive sign.
Villa at that point will be in the Championship, and despite Amavi's talent, his recuperation from injury and desire to repay the fans who have been so supportive of him, should combine to ensure he remains at the club next season.