Hearts winger Andy Driver remains available.
The Daily Record says Burnley have bid £2.5m rising to £4m but sources at Tynecastle revealed it was turned down.
Jambos owner Vladimir Romanov is reckoned to be holding out for at least £3m up front.
Burnley, relegated from the Premiership last season, had a £1.5m offer, rising to £3m, rejected earlier this month.
Driver, 22, is under contract at Hearts until 2013. He has attracted interest from a string of clubs but Burnley have been leading the race. They tried to capture him last year when Owen Coyle was still manager but their bid of just £750,000 was thrown out.
Chelsea, Middlesbrough, Wigan, Coventry, CSKA Moscow, Cologne and Twente Enschede have all been linked with the Oldham-born player.
