The 30-year-old was ruled out of the World Cup with a neck injury but after undergoing surgery it is hoped Rees will be back within ten weeks.
Davies confirmed the operation was a success and is keen to get the British & Irish Lions hooker back in time to play an integral role in their RaboDirect Pro12 season.
Scarlets' Heineken Cup campaign will get underway against French club Castres Olympique a week after the Ospreys clash, before they face last year's runners-up Northampton Saints and 2008 champions Munster in their group.
"The operation went very well," Davies said.
"Matthew is very good and we are hoping he will be available within eight to 10 weeks."
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