The Spain international has not trained for three days and has not travelled for the Premier League leaders’ match with the champions (17:30 GMT).
The news comes amid reports he is the subject of an offer to move to China that would be worth £30m a year.
Costa, 28, has scored 14 goals and provided five assists this season.
Chelsea declined to comment.
It is understood Blues owner Roman Abramovich is not interested in releasing him from his contract, which expires in 2019, and would not entertain the idea of being forced to do so.
Speaking in early January, Costa admitted he wanted to leave Chelsea last summer, but said he was now happy to stay.
Chelsea had been hopeful of agreeing a contract extension with the Brazil-born forward, but the dispute with fitness coach Julio Tous raises new doubts.
Costa joined the Blues for £32m in 2014, and was understood to be close to a return to former club Atletico Madrid after a difficult 2015-16 campaign.
“Did I want to go? Yes, yes, I was about to leave,” he said earlier this month. “But not because of Chelsea.
“There was one thing I wanted to change for family reasons but it wasn’t to be, and I continue to be happy here.”
Shortly afterwards, manager Antonio Conte said he believed the striker was now “completely focused” on “fighting for this club and for his shirt”.
He added: “When Diego decided to stay, I wasn’t concerned. He is showing great patience in the right way, in every moment of the game.”
Midfielders Jon Mikel Obi and Oscar recently left Chelsea for Chinese clubs – Tianjin TEDA and Shanghai SIPG respectively – while ex-Manchester City and United striker Carlos Tevez joined Shanghai Shenhua from Boca Juniors in a deal reportedly worth £310,000 a week.
Former England midfielder Jermaine Jenas on BBC Radio 5 live
Everything has been smooth sailing for Chelsea up to now. Imagine the faces of Manchester United boss Jose Mourinho, Liverpool manager Jurgen Klopp and Mauricio Pochettino at Tottenham. This is what they have been waiting for.
Another bid from the Chinese market seems to be rocking the boat of another top club. It’s a huge problem.
When these situations arise, the players are probably thinking they’ll go and do two years and then come back and play in the Premier League. Financially, they’re not just supporting their immediate family, they are supporting their whole family… aunts, uncles and cousins.
I’d still give Chelsea a good chance of winning the title even if they lost him. With the lead they now have, I think they can cope if they replace him.
You don’t want to keep players at your club who don’t want to be there. Yes, Costa has been a huge part of Chelsea’s success but he’s not Lionel Messi or Cristiano Ronaldo.
Everton winger Yannick Bolasie on BBC Radio 5 live
Diego Costa is a problem for any defender. He is strong, quick and doesn’t stop running. He sets the tone for all the other Chelsea players.
It’s frightening the way the Chinese market is acting right now.