Rodgers was appointed the Celtic manager in the summer of 2016 following the departure of Ronny Deila at the end of the 2015-16 campaign.
Under the former Liverpool and Swansea City manager, the Glasgow giants won the Scottish Premiership, the Scottish Cup and the Scottish League Cup last season.
Celtic also progressed to the group stage of the Champions League during the 2016-17 campaign, just as they have done this season.
Stoke midfielder Fletcher, who started his professional club football career at Manchester United and won the Champions League with the Red Devils in 2007-08, has named the Celtic players who have improved under Rodgers.
Fletcher plays with the aforementioned Celtic stars for the Scotland national football team.
“Stuart Armstrong has come on leaps and bounds, Scott Brown has always been a fantastic player but he is another whom I think took his game up another level under Brendan, and Craig [Gordon], Callum McGregor, Kieran Tierney and especially Leigh [Griffiths] have all shown a massive difference in their game,” Fletcher told The Glasgow Evening Times.
“The improvement has been there for everyone to see and while that has been great for Celtic it has also been great for Scotland and I think it is important that element is not overlooked.”