Rodriguez has scored five times this season.
Wenger will not be on the touchline for the next 3 games.
England international could return to the bench despite scoring a brace against Southampton.
Saints are looking to knock Arsenal out of a second cup this season.
The Netherlands international limped off last Sunday with an ankle injury.
Southampton reached the EFL Cup final without conceding a single goal.
Liverpool have lost their last two games at home.
Liverpool boss believes his side should have been awarded a penalty during Wednesday night's EFL Cup loss.
Shane Long nets in second-half stoppage time to seal the Saints' passage to Wembley.
Liverpool trail the first leg by a solitary goal.
Claude Puel also spoke on the possibility of signing a replacement for Jose Fonte.
Slaven Bilic and Mauricio Pochettino both addressed links with defender during Thursday press conferences.
France international has not featured for Liverpool this season.
Fonte handed in a transfer request at Southampton earlier this month.
Manchester United and Chelsea are reportedly interested in Van Dijk.
Saints host Jurgen Klopp's side in the first-leg match at St Mary's.
Southampton will leave Jose Fonte from the squad.
Coutinho will get some minutes when Liverpool face Southampton in the EFL Cup semi-final clash.
Captain handed in transfer request following the summer speculations linking him with Manchester United.
Matt Le Tissier says the Portugal international has behaved disrespectfully at St Mary's.
Charlie Austin is sidelined, with Shane Long scoring just once in the league this season.
Spurs come from behind to thrash 10-man Saints in a festive cracker at St Mary's.