The 31-year-old former Aston Villa man, who caught the eye in a cameo as substitute in the 1-1 draw at Turf Moor in March, has one year remaining on his contract at the King Power Stadium, but remains a key figure in Brendan Rodgers’ squad, featuring in the 20 for every match day squad last season.
Tamworth-born, Albrighton has been at Leicester seven years, helping the Foxes win the Premier League title in 2016 - but Burnley could hold an ace in the pack with midfielder Ashley Westwood, who is close friends with the wideman, the pair living opposite each other in their time together at Villa.
Burnley had led the race to bring in Ashley Young from Inter Milan as another side option, before his former club made him an offer he couldn’t refuse, leaving the Clarets with only Dwight McNeil and Johann Berg Gudmundsson as senior options in that area.
Burnley remain on the lookout for another centre back after the signing of Nathan Collins from Stoke City, with Nat Phillips of Liverpool, and long time targets Joe Worrall of Nottingham Forest and Middlesbrough’s Dael Fry on the list of options.
And the Clarets have also been linked with a string of right backs, the latest being West Brom’s Darnell Furlong, son of former Chelsea striker Paul.
The 25-year-old made 36 appearances for the Baggies last season as they were relegated from the Premier League.