Lund was mainly a reserve at Elland Road and was freed recently by Simon Grayson.
Burnley boss Owen Coyle will decide whether to offer him a contract after being tipped off by another former Whites 'keeper, Phil Hughes, now goalkeeping coach at Turf Moor.
Coyle let Hungarian Gabor Kiraly join Bayer Leverkusen on loan and he is unlikely to return, so he is in the market for some cover, according to The People.