However, with former Burnley player Laws also unavailable for comment, reports began to circulate he was edging ahead of O'Driscoll.
Laws would be a surprise appointment after being sacked by Championship strugglers Wednesday last month. The 48-year-old has previously managed Grimsby and Scunthorpe.
O'Driscoll, 52, had six years in charge of Bournemouth - where he spent the majority of his playing career - before taking charge at Doncaster in 2006.
He signed a new three-year deal at the Keepmoat Stadium last summer after leading Rovers into English football's second tier for the first time in 50 years in 2008.
The Clarets have yet to make any announcement over the identity of Coyle's successor, although, with some backroom staff having also moved with him to Bolton at the Reebok Stadium, they are thought likely to appoint quickly.
Chairman Barry Kilby said: "We are still interviewing, we are still looking."
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