Soriano had to cut short a bullpen session on Monday at Tropicana Field and will be evaluated by team physician Christopher Ahmad.
"We'll see what the doctor says," Soriano said.
Soriano last pitched on Friday against the Red Sox but has been experiencing discomfort since making back-to-back appearances on April 30 and May 1 against the Blue Jays. An MRI exam taken on Wednesday showed only mild inflammation.
In an unusual twist, Soriano said that he had received advice on Monday from Yankees executive vice president Felix Lopez, who told the right-hander he should think about taking a week or more off from pitching.
"He said, 'Let's see what happens -- you've got to take one week, 10 days, then come back and be 100 percent,'" Soriano said. "I think it'd be great. I've got to wait to see what the doctor says."
Soriano opined that the Yankees' relievers should not be blamed for the team's six-game losing streak.
"To me, I don't think the bullpen [is] the problem right now," Soriano said. "I think it [is] the hitters. [Those] things happen sometimes."
Soriano also said that his absence did not seem to have affected the team's fortunes.
"In these situations, how the team lost, that would not be the situation when I'm supposed to be in the game -- the eighth," Soriano said. "Everybody sees we've been losing by two, three runs. I don't think it would be the situation that I'd be in the game."
The Yankees had not been expecting to have Soriano available until Wednesday in Baltimore at the earliest; this latest issue makes a trip to the disabled list more likely.
With Soriano in limbo, the Yankees have continued to carry a 13th pitcher. They recalled right-hander Hector Noesi from Triple-A Scranton/Wilkes-Barre on Friday.
Soriano landed a three-year, $35 million contract to serve as Mariano Rivera's setup man after leading the American League with 45 saves last season for the Rays.
"I had good moments here," Soriano said before the Yankees' 6-5 loss to Tampa Bay. "I'll be happy to see a lot of good friends I have."