It is understood that a number of Premier League and Championship sides have been scouting the Irish-born midfielder in recent months.
McCann's current deal is due to expire in the summer, and he could be set to leave Turf Moor after more than 200 appearances for the Clarets.
Burnley are in talks with a number of players whose contracts expire this summer, but their Premier League parachute payments run out this year and they are looking to reduce their wage bill as a result.
McCann joined Burnley from Home Farm as a youth player in 2004 and has since gone on to become a stalwart for the club.
But with international ambitions also high on his list of ambitions, the 26-year-old is now considering his future.
Norwich, Wigan, Swansea, Middlesbrough and Bolton are among the clubs being linked with his services.