The Uruguayan, who tried to orchestrate a move away from Anfield, was the subject of two rejected bids from Arsenal, one of which is said to have been worth £40,000,001.
"I can understand why they were interested but we certainly were not going to sell to a rival and competitor," Rodgers said in a press conference. "I have seen an improvement from Luis with his maturity.
"It certainly wasn't an easy period, but we were very firm in our leadership that this was something we didn't want to do and that this was the place for Luis to showcase his talents."
Suarez is expected to start for the Reds in this Saturday's Premier League clash against the Gunners at the Emirates.