The $35 million setup man is experiencing recurring tightness in his right elbow.
"I'm going to throw a bullpen [session on Monday] and see how I feel," Soriano said after the Yankees' 7-5 loss to the Red Sox. "If everything goes fine, I'll be ready on Wednesday."
Yankees manager Joe Girardi said that the tightness Soriano feels is different than what he felt last week, when the hurler requested an MRI exam to ease his mind.
"He had a little pain before," Girardi said. "Today, he was a little sore; he said he had stiffness. That could have been because he hadn't thrown in five days."
Soriano appeared on Friday against the Red Sox after having not pitched in a game since May 8 in Texas. He has been experiencing some discomfort since appearing in back-to-back games on April 30 and May 1.
"Until he gets through the clear, it's an issue," Yankees general manager Brian Cashman said. "So until I'm not having to ask, 'How's he feel today?' it's obviously going to be a concern."
In the first year of a three-year deal, Soriano is 1-1 with a 5.40 ERA in 16 appearances. He saved an American League-leading 45 games last year for Tampa Bay.
"It's not easy for me," Soriano said. "I'm with a new team. I try to do my best. I can't right now. Nothing happens because I cannot pitch."