The Sun says Albrighton - a key man in the Foxes side that won the Premier League in 2016 - struggled for game time last season.
And Dyche believes he can lure the 31-year-old to Turf Moor because he has just 12 months left on his contract.
Albrighton would be a similar type of player and comes with the kind of solid experience that Dyche admires.
He would also be relatively cheap and give the Clarets options down both wings.
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