However, he could feature against Connacht on September 24, as the Welsh region look to recover from a slow start to the GUINNESS PRO12 season.
After finishing fifth last year hopes are high in southwest Wales, but back-to-back defeats against Munster and Edinburgh have left them tenth in the table.
Pivac's side visit high-flying Ulster on Friday, while Lee eyes up a return the following week.
"He's still on track for somewhere around the Connacht game. Failing that it'll be Treviso," Pivac said.
"Those sorts of injuries, they give a 12-16 week window, he's early on been put into the 14-week bracket, he's been progressing so well he's been put into the 12-week bracket.
"We're in consultation with the WRU, everyone is happy with his testing and we're on the same page. He's looking pretty good."
Guinness PRO12 Final 2017 Ticket Information: Fans can save up to 20% on selected tickets, and prices start at just €30 adults and €5 child, and be booked via www.ticketmaster.ie. For further information visit http://www.pro12rugby.com/final
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