Brentford's co-directors of football have been urged by manager Dean Smith to open talks with Alan Judge regarding a new deal.
But the former Republic of Ireland under-21 international has 16 months to run on his existing deal and was the subject of bids from Burnley and Sheffield Wednesday in January, according to Sky Sports.
The promotion-chasing pair were reportedly informed they would have to pay £8m for the 27-year-old.
Despite this, no new efforts have been made to keep Judge at Griffin Park, according to Smith.
"There is no update. It's in the hands of the co-directors of football and it will continue that way, but I've not been updated on anything," the former Walsall boss told Sky.
Asked if he would urge the club to open talks with Judge regarding an extension, Smith said: "Yes, I've waxed lyrical about him before.
"He's a very good footballer for us and, for the rest of the team as well, he adds that bit of experience."
After being priced out of moves for Judge, both Burnley and Wednesday moved onto alternative targets, with the Clarets bringing in free agent Lloyd Dyer and the Owls landing Aiden McGeady on loan from Everton, both until the summer.
However, the short-term nature of those deals suggests the pair could return for the former Blackburn Rovers player when the transfer window reopens.