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The recurring problem forced Clarke to miss the Champions Trophy and led to speculation that Australia's most prolific run-scorer in recent times could miss some of the five-test Ashes series in England, which starts at Trent Bridge on July 10.
The 32-year-old right-handed batsman said his back was improving and that he was looking forward to making his return against Somerset on Wednesday.
"My back is feeling better at the moment, it's still obviously a few days before that first practice game down in Taunton but if all goes to plan I'll be playing in that game," Clarke told reporters in London.
"We are going to continue to go one day at a time, the Australian physio (Alex Kountouris) is extremely positive that I am improving daily.
"I will continue to have work on it and I will just have to monitor it daily."
Australia will play a second warm-up match against Worcestershire next month before they launch their bid to win the Ashes back from England.
