Costa was nominated alongside Swansea duo; Nathan Dyer and Gylfi Sigurdsson, and also Aston Villa's Andreas Weimann.
Monk and Costa are set to go head-to-head on Saturday as Swansea travel to Stamford Bridge for a top-of-the-table encounter.
Swansea City boss Gary Monk has picked up the Manager of the Month award for August afte guiding his side to three wins from three, whilst Chelsea's Diego Costa has won the Player of the Month after scoring four goals.
The Welsh side have started the season on-par with Chelsea, and after starting the season with a shock 2-1 win against Manchester United at Old Trafford, The Swans then carried on their form by beating Burnley and West Bromwich Albion at the Liberty Stadium.
Monk has seen off Chelsea's Jose Mourinho, Aston Villa's Paul Lambert and Stoke City's Mark Hughes to the monthly accolade.
As for Player of the Month, Chelsea's new Summer signing, Diego Costa, picked up the award after he netted four times in three matches, including a brace against Everton during the nine-goal thriller at Goodison Park.