Sky Sports says the former Southampton right-back was all set to leave the Reds in the summer, only to suffer a cruciate knee ligament injury in pre-season.
He is recovering well though, and could be fit enough to complete a switch in the next month.
Clyne is out of contract at Anfield at the end of this season, and is likely to be allowed to depart for a nominal fee.
The 28-year-old has played 103 times for the Reds, but has seen his last two-and-a-half seasons decimated by injury.
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