Reported interest in Basel's Egyptian wide-man Mohammed Salah had led to speculation that Rodgers is contemplating sending Sterling out on loan to continue his development with regular first-team football.
But speaking at his post-match press conference following Liverpool's 2-0 FA Cup third-round victory over Oldham, Rodgers admitted he had no idea where the reports had emanated from and dismissed the idea that Sterling could leave the club.
"I don't know where it has come from. I don't think you let a player who's in your team and playing exceptionally well go on loan," Rodgers said.
"It must have been one of the media guys whose entry checked four or five months later. I think it must have been in the entry for four or five months and he hasn't looked at it and he's just picked it up and put it in the paper.
"He (Raheem) was excellent today. His strength and pace was frightening today so no he won't be going anywhere," Rodgers added.
Sterling became the third-youngest player in Liverpool's history after making his debut in the club's Premier League game against Wigan in March 2012 aged 17 years and 107 days.
The former QPR youngster made his England debut later that year in November in England's 4-2 defeat against Sweden in Stockholm.
The 19-year-old has started Liverpool's last nine matches.