The Swansea City man is known to Sean Dyche and has played for Burnley twice before.
Celtic boss Brendan Rodgers is said to be considering alternative targets after deciding not to bring the American to Parkhead.
Arsenal came out 3-2 winners in the game against Swansea City at the weekend.
With the American now in charge, we take a look at three Swansea City players who could potentially benefit the most from this change in management.
The Swans midfielder was left frustrated after their 2-0 defeat to Hull City
The midfielder moved to Newcastle United in the January transfer window.
The Tottenham Hotspur and Swansea City stars compared...
He is joined in the top five by the likes of Etienne Capoue, Jordan Amavi and Jack Cork.
Players from Aston Villa, Swansea, Nottingham Forest, Sunderland and Sheffield Wednesday feature.
Cork, who signed from Southampton during the January transfer window, thinks the side can back up an impressive season with another next year.