Brentford have rejected an offer from Sheffield Wednesday for Alan Judge, according to Sky sources.
And rival Championship promotion-chasers Burnley are also understood to be interested in the 27-year-old Republic of Ireland international.
It is understood Wednesday's offer did not come close to meeting the Bees' valuation of the player, who has been outstanding in the division this season.
Judge's contract expires in 2017 and Brentford are believed to be keen to tie him down to a new deal.
When asked about potential interest in him last month, new head coach Dean Smith said he would tell the club's hierarchy to keep the attacking-midfielder.
He said: "I would certainly be telling the club that, if we did [have any bids], I would want to keep him. Judge has been a big player and a pleasure to work with since I've been here."
Judge signed for Brentford from Blackburn Rovers in the summer of 2014 following an impressive loan spell, and he has scored 13 goals in 63 appearances for the west London club.