With the Guinness PRO12 season less than six weeks away, it's unlikely that the pair will be able to feature in Ospreys' opener against Zebre on September 2, with both still requiring further work before being back in contention.
Lydiate was named by Warren Gatland as Wales' captain for their clash with England in May, but a double injury blow to his shoulder and hamstring forced him off in the first half, ruling him out of the summer tour to New Zealand.
While fellow back-rower King was able to face the All Blacks, a neck injury prematurely ended his trip after featuring 21 times for Ospreys in the 2015-16 Guinness PRO12 campaign.
"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," said Ospreys medical performance manager Chris Towers.
"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.
"James is recovering from a neck injury he picked up in New Zealand.
"He's progressing well but we will continue to observe his recovery and progress over the coming weeks before we will be in a position to confidently predict when he will be available for selection."
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