Yankees manager Joe Girardi said before Sunday's 7-5 win over the A's that Soriano could pitch on Monday as well.
"We're looking at that," Girardi said. "I just want to see how he feels today. If he feels good after today and tomorrow, it is very possible he would pitch again on Monday."
Girardi said the quality of Soriano's outings will be the main factor in deciding when the reliever returns.
"We want to see him throwing the ball well and that his stuff is back," Girardi said. "I think that's important. So to say that if he goes back-to-back, is that all you have to see? No. We have to see the quality of the stuff more important than the back-to-back."
Soriano, who has been on the disabled list with right shoulder inflammation since May 27, threw a 16-pitch inning on Thursday for Class A Tampa, giving up one run on two hits.
Infielder Eric Chavez, meanwhile, went 1-for-2 with a two-run home run on Saturday as Tampa's designated hitter and was set to start there on Sunday.
Girardi said on Friday it was possible that both Soriano and Chavez -- who has been on the DL with a bone bruise in his left foot since May 6 -- could return to the Yankees during their current 10-game homestand.
"For both of them, things are looking up," Girardi said on Sunday.