The 30-year-old striker moved to the Championship club on a short-term loan deal in September.
Murray's loan agreement now has a recall option included, but he is expected to stay with the Royals until the New Year.
When asked about the loan deal, Parish told South London Press: "There's certain things in there that I wouldn't want to comment on.
"It's all up in the air - but he has definitely not signed for Reading."
Murray has scored three goals in six appearances for the Berkshire club.