The Roma and Italy great signed with Boca last week after his 18-season stay with the Serie A giants came to an end.
However, De Rossi must wait for his debut, with the club eyeing their Copa Argentina clash against Almagro on August 13 as a possible first appearance for the 36-year-old.
"We are testing him. He is in an evaluation period," Boca coach Gustavo Alfaro told a news conference after his side drew 0-0 with Huracan on Sunday.
"We are evaluating him because he has a really good attitude and he shows himself eager to work. We are looking at his physical conditions.
"So, based on this I was talking with his trainer to see how possible it is to get him ready to play against Almagro in the Copa Argentina. That's in 18 days, it was 18 days when I talked to him. I asked him if we can get him fit in 18 days.
"We are working on this premise, so he can get onto the pitch at that time so he can play."