Maxi arrives for Liverpool medical
The Argentine internatinal is expected to sign an 18-month contract with Rafael Benitez's side, and will be present for the Reds' FA Cup Third Round replay against Reading on Wednesday night.
The 29-year-old has made more than 100 league appearances for the rojiblancos since arriving from Espanyol in 2005, where he also clocked up a century of La Liga outings.
He has been capped 35 times by Argentina, scoring 10 times - the most memorable of those a stunning volley at the 2006 World Cup that knocked Mexico out of the tournament.
Rodriguez will become Liverpool's second signing from Atletico Madrid in recent years, following the arrival of Fernando Torres in 2007, and will team up with fellow countrymen Javier Mascherano, Emiliano Insua and Gerardo Bruna.
He has already scored at Anfield, netting in a Champions League group game for Atletico against Liverpool in November 2008.