"I think that's realistic," manager Joe Girardi said, "if he feels good and throws the ball well."
Bruney was placed on the 15-day disabled list with a strained right elbow flexor on April 25, and he came through bullpen sessions on Wednesday and Friday with no reported problems.
Bruney, who has been New York's usual setup man, said he threw close to 100 percent in Friday's 35-pitch session and was confident in how his arm feels.
"I feel as good as I can right now," the reliever said. "I was getting after it [on Friday]."
Bruney has made no secret of his frustrations in a tedious rehab of rest and ice, and was anxious to get back into the bullpen on Tuesday and avoid making multiple rehab appearances.
"That's my goal," he said. "But that's the manager's decision. [But] I guess it is my decision, because if I throw well, then it probably will only be one [game]."
Injured pitcher Chien-Ming Wang (abductor muscle weakness) is scheduled to start for Scranton on Sunday, but Girardi said the Yankees will fit Bruney in regardless.
"Even if Wang throws 70 pitches in eight innings, we've still got to get Bruney in there," Girardi said.
Injured outfielder Xavier Nady is slowly making his way toward a rehab start, testing his injured right elbow on Friday with 26 full swings.
"I think it's realistic to think that if everything goes according to plan, he could go to [Tampa, Fla.] when we left [for a road trip on May 25]," Girardi said.
Nady has been on the DL since April 15 with an injured ulnar collateral ligament, and he has already missed the past 26 games.
On Saturday afternoon, Nady told reporters he felt 85-90 percent and planned on swinging the bat again sometime in the early afternoon.
When Nady does go to the club's Spring Training facility in Tampa, Girardi said his assignment would be similar to that of Alex Rodriguez, who started in a hitting role first.
Brittany Ghiroli is a contributor to MLB.com. This story was not subject to the approval of Major League Baseball or its clubs.