Hughes is now at the centre of a managerial tug-of-war after Manchester City also made an approach for him.
The former Manchester United striker was given permission by Blackburn on Monday to speak to City regarding the possibility of replacing Sven Goran Eriksson at Eastlands.
But according to Sky Sports News, Hughes is one of two names in the frame to replace Avram Grant in the Stamford Bridge hot seat.
Senior Chelsea figures met outside the country on Monday to discuss the appointment of a new boss, with Hughes and a foreign candidate in contention to succeed Grant.
Chelsea's hunt for their next manager has now 'seriously gathered pace' and a decision is understood to be imminent.