The Denmark international has made 34 appearances in all competitions this season and his contract is set to expire in the summer.
It's believed he'll be joining Barcelona on a free transfer after nine years at Stamford Bridge, but it could be an ugly exit.
Per the Daily Mail, Christensen told manager Thomas Tuchel he didn't feel ready to play on the morning of the game.
The 26-year-old played 90 minutes in Wednesday's 3-0 win over Leeds United alongside Antonio Rudiger and Trevoh Chalobah.
It's likely Christensen would've started at Wembley over Chalobah if available, but instead Thiago Silva took his place.
Sources close to the former Borussia Monchengladbach loanee claim he'd been feeling ill in the days leading up to the game and had explained that to Tuchel.
His withdrawal at the eleventh hour still shocked his Blues teammates, however.
Chelsea were beaten 6-5 in the penalty shootout after an absorbing 120 minutes of action finished 0-0.
Mason Mount had his penalty saved by Alisson and Kostas Tsimikas sent Edouard Mendy the wrong way to secure Liverpool's second trophy of the season.
It's also their second win over Chelsea at the national stadium in the last three months, having won the Carabao Cup in similar fashion back in February.
The Blues have now lost three FA Cup finals on the bounce, but Tuchel was 'proud' of his players after their showing this past weekend.
He explained: "Like in the last final, the Carabao Cup, no regrets. I told the team I was proud.
“We played 240 minutes across two finals against maybe the most dangerous attacking team in the world and it's 0-0. We lose on penalties and we are disappointed and sad, but at the same time proud because we showed everything that we need.
"I was sure during the match the momentum was on our side but unfortunately I was not right."
Chelsea have two games remaining in the Premier League as they look to secure their place in next season's Champions League.
Christensen isn't the only defender leaving, as Antonio Rudiger is likely to move to Real Madrid as a free agent.
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