Derby County are believed to have had a £1.4 million bid for Kilmarnock striker Steven Naismith turned down.
The new bid, which came from a non-identified promoted Premiership club, dwarfs the £600,000 offer that Rangers tabled at the end of last week, which was also rejected by the Rugby Park club. Birmingham, Derby and Sunderland, all promoted from the Coca-Cola Championship this season, are the most likely suitors.