According to Lancashire Live, both of Burney’s prospective new owners ALK Capital and Mohamed El Kashashy want to retain Sean Dyche amid Derby County links.
Derby are currently manager-less after Phillip Cocu’s exit last month.
Several names have been linked with the Pride Park job including John Terry and Sam Allardyce.

But the latest from Alan Nixon from The Sun claims Sean Dyche is also a shock candidate.
Derby are also going through a takeover. The prospective new owner is the cousin of Manchester City’s Sheikh Mansour, and big funds could be available for the Rams.
Burnley, however, seemingly have no interest in losing their popular manager.
Lancashire Live claim the potential new buyers are looking to build the club around Dyche following his success at Turf Moor and instead a new improved contract could be in order.
Dyche’s current deal with the Clarets expires in the summer of 2022.
Derby currently sit second from bottom in the Championship table. The Rams are in danger of dropping down to the third division for the first time in over 30 years.
Wayne Rooney is currently in sole interim charge. While some supporters may wish to have a more experienced man in charge, signs of improvement are there.
In Rooney’s three games in sole interim charge, Derby have picked up five points including just their second win of the season in the 1-0 triumph at Millwall on Saturday.

The 35-year-old has made no secret of his desire to become a manager.
Rooney has the big profile, a potential list of strong contacts and experience of playing under some of the best such as Sir Alex Ferguson and Jose Mourinho.
Also see: Rio Ferdinand reacts on Twitter to Wayne Rooney’s first win as interim Derby boss
Also see: ‘Absolute monster, crucial’: Some Derby fans rave about Rams ace in Millwall victory