Suarez was strongly linked with the likes of Arsenal and Real Madrid, after having asked for a move away from Liverpool over the summer.
"Suarez was very keen to leave Liverpool in the summer and I have no doubt that he will look to get away once again," said Aldridge.
"So why try and get him to commit to the club now, so soon after he did the dirty on them with his bid to join Arsenal?
"Liverpool chief executive Ian Ayre may have told the media he would consider a new contract for Suarez in a bid to dampen down any fresh speculation over the future of the striker.
"But if Liverpool fail to qualify for the Champions League once again, I'm sure Suarez will want to leave and I would advise my old club to get as much money for him as possible and rebuild the team with the new funds."
A new deal could reportedly see Suarez earn around £160,000-a-week.