Dundee United have rejected an offer in the region of £900,000 from Celtic for striker Nadir Ciftci.
And sources at Tannadice have told BBC Scotland that it would take a bid in excess of £1m for them to part with the 23-year-old.
The Turkish-born forward scored 16 goals for United last season and is under contract for another year.
Celtic may face competition from Middlesbrough, who are weighing up an approach for Ciftci.
He joined United from Dutch side NAC Breda in July 2013 on a two-year deal and extended that contract by a further 12 months.
However, he rejected the offer of another one-year extension in June, saying he wanted a "new challenge" in 2016.
Ciftci is due to answer a charge of "excessive misconduct" next month after the Scottish FA accused him of biting Dundee midfielder Jim McAlister on the leg during the final match of last season.
The player could face a lengthy ban if found guilty but United say they are "fully supportive" of the striker.
Celtic signed midfielders Stuart Armstrong and Gary Mackay-Steven from United in January.