According to the Richmond and Twickenham Times, The Bees would currently fail to satisfy Premier League stadia standards should they achieve the possible back to back promotion.
The club is required to submit plans to football chiefs by the end of January and the club are keen on remaining at Griffin Park.
Chief executive Mark Devlin tweeted: "We have applied 4 planning permission to cover the New Road concourse. If we get the green light would hope to do work in summer."
The Bees plans for a new 20,000-capacity stadium at Lionel Road, near Kew Bridge, is expected to be ready in 2017.
Mr Devlin told the BBC earlier this month: "It is not inconceivable that we could put seats on the terracing.
"It would reduce the capacity so we are also looking at coming up with creative ways of adding additional seats.
"The media facilities are still a tad spartan - media is probably our biggest challenge, along with the changing facilities."
Brentford are one of six sides sereated by just four points at the top of the table and are currently 5th.