Owen's current contract expires next summer, and is in talks to extend his deal at St James' Park.
However, The Guardian reports that Newcastle are reluctant to match or increase his current £105,000-a-week wage as they look to cut costs.
Owen and his representatives know that he could get a better deal elsewhere should he not sign a fresh contract, and could begin negotiations with other clubs from January.
The paper claims Owen would rather stay at Newcastle, but is negotiating from a position of considerable strength considering the offers he might receive from elsewhere.