Forest's sacking of Stuart Pearce yesterday has destabilised the club and Burnley are hoping to capitalise on this.
Attacking midfielder Lansbury has been a first-team regular for the Reds this season, but Sean Dyche's side believe they can convince them to part with him.
Forest need to raise funds given their struggles to fit in with Financial Fair Play and they may feel that Lansbury is a expendable player, should they be offered a sizeable sum.
Impact for Forest?
Lansbury has actually been one of Forest's most disappointing performers this campaign but, on his day, he is one of their best players.
Most people expected Lansbury to push on this term and make himself an influential player at the City Ground, but his form has fallen short of his best.
The 24-year-old has scored just five times in 22 matches for the Reds and will need to raise those standards if he does complete a move to the Premier League.