The new Magpies boss arrived at St James' Park with speculation already rife over the future of the England striker, with both Manchester United and his former club Liverpool said to be heading the chase for his signature.
Two injury-hit years have restricted Owen to little more than a handful of games for the club since his £17million move from Real Madrid in the summer of 2005.
He has a release clause believed to be £9million and Allardyce said: "If Michael wants to leave, there's nothing I can do about it, especially if another club triggers his release clause.
"At the moment, we are benefiting from a release clause to get Joey Barton. But we could also suffer because of Michael's."