West Brom have slapped a £1 million compo price on manager Tony Mowbray.
The News of the World says Celtic are still considering an approach for their former player but may be put off by the fee.
Boss Mowbray, 45, has been told to trim his squad as the Baggies start life in the Championship after relegation from the Premier League.
And he is said to fancy the big challenge of leading Celtic next season.