Dummett was a consistent performer for Newcastle in the Premier League, but his position in Rafael Benitez's side could be under threat with the signing of Ciaran Clark and the imminent arrival of Brendan Galloway on loan from Everton.
Burnley are looking to strengthen their defence as they prepare for their return to the Premier League, having gained promotion last season and returning to the top tier of English football at the first time of asking.
Geordie Dummett can also play at centre back and has had loan spells at Gateshead and St Mirren, before claiming the left-back position at Newcastle.
Although a return to the Premier League may make Dummett consider leaving his boyhood club, the Chronicle report that Newcastle are not looking to sell the Welsh international and still believe he has a future at St James' Park.
Dummett is a more traditional full-back, often reluctant to go forward like most modern defenders, and has scored two Premier League goals for Newcastle, netting in home draws against Liverpool and Manchester United.
Burnley boss Sean Dyche is keen to add Premier League experience to his squad and the versatile Dummett fits the bill.