Prior to Saturday's game against the Mets, Padres manager Bud Black indicated that Street could report to one of the club's Minor League affiliates to face live hitting and build his endurance.
"He's encouraged by his progress," Black said. "We're looking forward to getting him on the mound."
Street took another step forward in his rehabilitation on Saturday, when he played long toss in the outfield at Citi Field. He's been able to increase both the time he's throwing and the distance.
He'll likely throw a bullpen session in the coming days, and if he emerges healthy, he could be sent out to pitch in games sometime next week.
Street, who was 4-for-4 in save opportunities, suffered the injury while throwing during the 10th inning of a 9-8 loss to the Marlins at Petco Park on May 4.
Dale Thayer has successfully converted all five of his save opportunities since filling in for Street, heading into Saturday.