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Lydiate was ruled out of his country's tour of New Zealand in June after sustaining injuries against England at Twickenham in a match he started as captain with Sam Warburton absent.
Ospreys have three pre-season friendlies pencilled in for August, before starting their 2016-17 Pro12 campaign against Zebre on September 2, with Lydiate appearing to have a chance of featuring against the Italians.
Ospreys medical performance manager Chris Towers said: "Dan is recovering well from surgery to reconstruct the shoulder ligaments he damaged in the England game.
"In addition, he also injured his hamstring in the same match.
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"He's recovering well on both fronts but still has some work to do.
"We'll be looking to up the ante through this next batch of pre-season with a view to being able to confirm a return to play date in the next few weeks."