Gerrard was left out of Liverpool's starting XI for the first time in the Premier League this season for Saturday's 1-0 victory over Stoke City.
The 34-year-old's recent performances had attracted criticism from certain quarters, with Liverpool having gone five games without a win in all competitions before the hard-fought success against Stoke.
Saturday's fixture marked the 16th anniversary of Gerrard's first-team debut for Liverpool, and various reports had suggested that he was unhappy with Rodgers for omitting him.
However, the former England skipper took to social media on Sunday to rubbish such speculation.
Posting on his official Instagram account, with an accompanying photo of himself and Rodgers, Gerrard wrote: "Just to set the record straight talk of a fall out between us 2 is NONSENSE...have a nice Sunday #together #solid #ynwa."
Gerrard's future at Anfield remains uncertain, however, with Rodgers telling his post-Stoke media conference that there has been no movement on negotiations over a contract extension for his skipper - whose current deal expires at the end of this season.
"There's no update I am aware of - I think the club is talking with Steven's representatives," said the Northern Irishman.
