The centre-back has been in fine form but does not join team-mate Jack Cork in Gareth Southgate's squad.
Tottenham Hotspur's Joshua Onomah is thriving for Aston Villa.
West Bromwich Albion are reportedly set to be disappointed in their pursuit of Manchester United midfielder Michael Carrick.
Jack Cork was man of the match for Burnley on Monday, but cannot get into the England team, unlike his Liverpool and West Brom counterparts.
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.