The Baggies are eager to bring their former trainee back to The Hawthorns and talks remain ongoing, PA understands.
Sawyers has been a long-term target for the Baggies and new boss Slaven Bilic has given the green light for his return.
Albion are confident they will be able to wrap up a deal as they continue negotiations with Brentford.
The 27-year-old left Albion on a free to join Walsall in 2013 having failed to make a senior appearance for the Baggies.
He impressed during a three-year stay at the Banks’s Stadium and moved to Brentford on a free transfer in 2016.
Sawyers has scored seven goals in 135 games for the Bees and has one year left on his current deal.
Celtic were keen on taking him to Scotland and had a bid rejected earlier this month, while Aston Villa’s former Brentford boss Dean Smith remains an admirer.
Sawyers, a St Kitts and Nevis international, made 46 appearances for Brentford last season as they finished 11th in the Sky Bet Championship.
Albion – who were beaten play-off semi-finalists last season – are looking to beef up their forward line after losing Jay Rodriguez to Burnley and seeing Dwight Gayle return to Newcastle after his successful loan.
Brentford could also lose striker Neal Maupay with the forward linked with Aston Villa and Sheffield United after scoring 28 goals last season.