The giant centre-back is being heavily linked with a move to Yorkshire this week.
Burn, who stands an imposing 6ft 7in tall, has been in and out of the Fulham first-team since making his breakthrough in 2013.
However he has started Fulham's last five games and has played 18 times for the Cottagers this season - so it would seem am ambitious move from Nigel Adkins and co.
Burn is however out of contract in the summer and it remains to be seen how new manager Slavisa Jokanovic believes Burn will fit into the team in the long run.
It seems Sheffield United will keep tabs on his development this month and should he struggle for regular football toward the end of January make a move to sign the player.
Sheffield United are currently eight in the League One table after a recent upturn in form and will be hoping to strengthen their squad this month to ensure of a play-off place come the end of the season.