The Sun says City owner Thaksin Shinawatra is anxious to seal a swift deal just in case managerless Chelsea turn to boss Hughes as a replacement for Avram Grant.
But Ewood chairman John Williams will not allow his club to be trampled on.
Rovers squeezed £3m out of Newcastle when Graeme Souness left in 2004.
And Sparky still has two years to run on his £1.5m- a-year deal at Ewood Park.
Welshman Hughes has told Rovers he is keen on a fresh challenge after four years working at Ewood Park.