Burnley will allow Chris Eagles and Tyrone Mears consent to speak to Bolton after accepting a joint bid in the region of £3million.
Winger Eagles and right-back Mears are in the final year of their contracts at Turf Moor having been signed by former Clarets boss and now Trotters manager Owen Coyle.
Burnley had hoped to convince the pair to sign extensions on their current deals, but a move to the Reebok Stadium now appears likely.
The Championship club confirmed the development after the duo were left out of Saturday's pre-season friendly with Torquay.
A statement on the Clarets' official website read: "Burnley can confirm that Bolton Wanderers have been given permission to speak to Tyrone Mears and Chris Eagles.
"A fee in the region of £3m has been agreed for the Clarets duo, who are set to enter the final year of their current contracts.
"Burnley had hoped to persuade the players to sign extensions to their present deals. However, with the players expressing their desire to return to the Premier League ... (we) regrettably accepted this offer from Bolton.
"The funds from Eagles and Mears' expected departures will be used to strengthen the squad, with further transfer developments expected early next week."
Former Manchester United winger Eagles, who joined Burnley from Old Trafford in 2008, had been linked with several top-flight clubs this summer including Queens Park Rangers, Everton and Swansea.
The Clarets have already allowed three players to depart this summer - with Chris Iwelumo offloaded to Watford, Graham Alexander released and Clarke Carlisle loaned to Preston.