The Scottish duo's contracts expire next month and they have not been offered new deals.
Howe said: "We thank both players for their efforts during their time at Turf Moor and wish them all the best in their future careers."
Thompson spent almost three seasons with the Clarets following his arrival from Cardiff in August 2008.
McDonald joined from Dundee in June 2008 and helped the club to promotion in his first season at Turf Moor.



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