The 30-year-old came through the youth set-up to play three first-team seasons for the Rosario-based side before moving to Espanyol in 2002.
"When I left here, I knew I was coming back," Rodriguez told Argentinian newspaper La Capital.
"The president (William Lorenzo) called me and I said yes. Now it depends on the contract I have in Liverpool, maybe that can be loosened a little."
Despite a successful end to the campaign with Liverpool, scoring two hat-tricks as he hit seven goals in three matches, Rodriguez is likely to be only a fringe player next season.
As manager Kenny Dalglish looks to freshen up his squad and bring in younger players, Rodriguez's age is likely to count against him and, as one of the club's higher earners, owners Fenway Sports Group would prefer to get better value for money from new signings.
However, the player would have to take a significant drop in salary in order to return to his homeland.