Liverpool are the only top-flight team to maintain a 100 per cent record after three rounds of matches, with the striker netting the winning goals in each victory
Rodgers has led Liverpool to two straight victories from their opening two fixtures and continued their impressive start with a home win against Manchester United at Anfield on September 1.
|10/1||Liverpool are 10/1 with bet365 to beat Swansea by three goals
Both 1-0 victories were inspired by the encouraging form of England international Sturridge, who won the award for the first time in his career having led the line in the absence of the suspended Luis Suarez.
The Merseyside club have made their best start to a league campaign for five years, with Rodgers leading them to first place with the only team still boasting a 100 per cent record.
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 continue their league campaign with an away trip to Rodgers' former club Swansea City on Monday night, although Sturridge is a doubt with a thigh injury.