The 30-year-old was absent for his club side's 25-17 triumph over Leinster in Dublin on Friday due to an ankle problem, potentially opening the door for England skipper Dylan Hartley to earn a surprise call-up.
Reports in the British press earlier this week suggested that Hartley was waiting by should Owens be declared unfit to play a part in this summer's tour, but Pivac expects his player to soon be back on the field.
"Ken is improving every day and is very upbeat," BBC Sport quotes him as saying. "By all accounts he is progressing well. We would like him to improve for next weekend but we are not sure there is the time."
The Lions fly out on May 29, five days before their first tour match against New Zealand Provincial Barbarians.