Grigg, 23, has spent the past season on loan at the Dons, scoring 22 goals in 50 appearances, and the Sky Bet League One club, who were promoted earlier this month, are keen to make the deal permanent.
But Sky Sports understands the Dons’ initial offer has fallen short of the Bees’ £1m valuation.
Grigg, who has a year left on his current Bees contract, signed a three-year deal when he joined from Walsall in 2013 for an initial £325,000 – a fee that was decided by tribunal and rose to £405,000 after Brentford were promoted to the Championship.
A further £250,000 was due if Brentford were promoted to the Premier League and Walsall will also land a 20 per cent sell-on fee if Grigg is transferred to another club.
Grigg was a Walsall trainee and scored 28 goals in over 100 appearances for the Midlands club.