Odegaard will miss the English Premier League match with Manchester City on Sunday, and Arteta said he did not know when the playmaker would be available again.
The Spanish international remains the most expensive goalkeeper of all-time after his £71 million ($94 million) move from Athletic Bilbao to Chelsea in 2018.
De Rossi is loved by Roma fans as a local boy turned World Cup winner who played almost his entire career for his hometown club.
Enzo Maresca was lured from Leicester after winning promotion to the Premier League last term, but cynics suggested he would soon become the latest victim of Chelsea's blame game.
Jasmine Paolini and veteran Sara Errani overcame Iga Swiatek and Katarzyna Kawa 7-5, 7-5 to send the four-time champions through to Wednesday's final.