Suarez repeatedly claimed that he wanted to leave Anfield during the summer, first citing too much media attention, and then stating that he wanted Champions League football.
The Reds striker eventually stayed with the club after two failed bids from Arsenal, but Aldridge feels that the saga has not yet run its course.
"Suarez was very keen to leave Liverpool in the summer and I have no doubt that he will look to get away once again," Aldridge told The Metro.
"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.
"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?"
Suarez returned to Premier League action from his 10-game ban by scoring twice in Liverpool's 3-1 win over Sunderland on Sunday.