Rodriguez is scheduled to have a medical before signing an 18-month contract.
The winger will watch Liverpool’s FA Cup third-round replay against Reading at Anfield before returning to Spain to tie up the final details of his departure from Atletico Madrid.
Rodriguez, 29, still has to agree his pay-off from Atletico but could be back in England by the weekend to figure in the squad that will travel to Stoke on Saturday.
Liverpool manager Rafael Benitez had hoped the £1.5million deal could have been completed last week, but the former Newell's Old Boys and Espanyol player was unable to finalise the details of his departure.
The arrival of Rodriguez - a close friend and international team-mate of Reds midfielder Javier Mascherano - will follow the departures from Anfield of Andrea Dossena to Napoli and Andriy Voronin to Dinamo Moscow.
Those two deals have brought in funds totalling £6.5million, and Ryan Babel's name could soon be added to the list of departures now Benitez has been assured that he can have the potential £10million fee to strengthen his squad during this transfer window.
Benitez had previously been told to wait until the summer before spending on new additions.