West Bromwich Albion are refusing to be bullied in the transfer market this summer.
Burnley want to sign the pair and made a combined £25 million offer in June.
But that figure came nowhere close to what West Brom want, per Sky Sports News.
Dawson has handed in a transfer request and refused to go on the club's recent training camp to Portugal.
But Rodriguez was part of the traveling party, despite also wanting to leave.