The Colombian sustained a calf knock during the warm up, prior to the 2-1 defeat at home to the Villains earlier this month, and although Carlo Ancelotti stated last week that the injury is "minor", the 29-year-old is not expected to be fit in time to return to the first-team squad.
Jean-Philippe Gbamin and youngster Tyler Onyango are the only other absentees for the Toffees as they head to Villa Park due to respective knee and ankle problems.
Central midfielder Abdoulaye Doucoure - who was back among the substitutes for the win at West Ham United on Sunday, after missing the last two months with a fractured foot - is in contention to feature on Thursday.
Ancelotti decided to use a 3-5-2 formation against the Hammers and the Italian may choose to stick with this setup against Villa, as opposed to the 4-2-3-1 lineup that he started with in the reverse fixture.
Mason Holgate could be recalled to the side at the expense of Yerry Mina to play alongside Michael Keane and Ben Godfrey in the heart of the defence, while Seamus Coleman and Lucas Digne are set to operate in wing-back roles.
Gylfi Sigurdsson - who has played more matches for Everton than any other player so far this campaign - is likely to keep his place in the side, providing much-needed creativity in Rodriguez's absence.
The Icelandic international, along with Allan, could be joined in midfield by either Tom Davies or Andre Gomes, while Richarlison and Dominic Calvert-Lewin are set to lead the line once again.
Everton possible starting lineup: Pickford; Holgate, Keane, Godfrey; Coleman, Gomes, Allan, Sigurdsson, Digne; Richarlison, Calvert-Lewin
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