The Uruguayan has since apologised for his actions and was fined two weeks' wages by the club, but there have been several calls for the Reds to move their 30-goal striker on in the summer.
However, writing in his Liverpool Echo column, Aldridge has said that he will not be one of the people calling for the former Ajax man to be sold.
"A lot of people won't agree with me and will argue he's damaged the club's reputation once too often but the bottom line is he's absolutely vital to Brendan Rodgers' team," he wrote.
"If we want to be successful as a club, then we need to build on what we've got. If we want to challenge for the top four next season we can't afford to be selling our best players.
"You can't condone what Suarez did on Sunday. Biting Branislav Ivanovic was a terrible thing to do and now he will have to suffer the consequences. But I don't go along with the idea that enough is enough and that Liverpool should be looking to sell him this summer. Yes, I want him to stay."
Suarez accepted a charge of violent conduct from the Football Association yesterday.