Gerrard was left out of the starting XI for his side's 1-0 win over Stoke on Saturday, with the match falling on the 16th anniversary of his first-team debut.
Rodgers, who sent the midfielder on as a second-half substitute, admitted afterwards he was not aware of the landmark, but described the 34-year-old as a "wonderful man".
But that did not stop talk of tension between the pair, with Gerrard's contract up at the end of the campaign and consistent criticism this term of his performances in a holding midfield role.
The former England captain dismissed that notion via his Instagram account, posting an image of the pair laughing together during a training session, accompanied by an unequivocal message.
It read: "Just to set the record straight media talk of a fall out between us 2 is NONSENSE ..have a nice Sunday ??#together#solid#ynwa".
Rodgers has spoken previously about easing Gerrard's workload, particularly with the Reds having additional Champions League duties this season, but this was the first time this season the midfielder has not started a league match.
He played the full game in midweek against Ludogorets and then 15 minutes against the Potters, after which Rodgers praised his impact from the bench.
Source: PA