Owen is struggling with a thigh injury.
Allardyce told the Daily Mail: “It doesn’t look as encouraging as we first thought.
“The tear in the muscle hasn’t healed as quickly as we would like, so there’s no point in making any rash decisions just to get him fit for the start of the season.
“It’s about getting him 100% for playing matches on a regular basis. That’s why it has been more disappointing for him that he’s missed pre-season games more than training.
“He’s done enough training to last him a lifetime.”
