Liverpool is the only top-flight team to maintain a perfect record after three rounds of matches, with Daniel Sturridge netting the winning goals in each victory.
Rodgers has led Liverpool to three straight victories, punctuated with a home win against Manchester United at Anfield on Sept. 1. Liverpool's fine start to the season began with a home win against Stoke City before picking up a further three points on the road at Aston Villa.
All three 1-0 victories were inspired by the encouraging form of England international Sturridge, who win the award for the first time in his career having led the line in the absence of the suspended Luis Suarez.
The Merseyside club has made its best start to a league campaign in five years, with Rodgers leading the Reds to first place with the only team still boasting a perfect mark. Rodgers, who is also yet to see his side concede a goal this season, picks up the award for the second time in his career but his first since joining Liverpool in June 2012.
Liverpool continues its league campaign with an away trip to Rodgers' former club Swansea City on Monday, although Sturridge is a doubt with a thigh injury.