The club already has reached agreements with at least 28 of them, though it has not confirmed the deals.
Griffin (Ga.) High School shortstop Cornelius Randolph, who was selected with the 10th overall pick in the first round, tweeted Monday evening that he is headed to Philadelphia. He later deleted the tweet. Randolph is expected to take his physical Tuesday.
Second-round pick Scott Kingery, fourth-round pick Kyle Martin, seventh-round pick Luke Leftwich and 12th-round pick Skylar Hunter were some of the players in Philadelphia on Monday. They have agreed to deals.
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The Phillies have reached agreements with 13th-round pick Zack Coppola ($85,000 signing bonus), 17th-round pick Kenny Koplove ($75,000), 22nd round pick Sutter McLoughlin ($50,000) and 24th-round pick Zach Morris ($30,000).
Penn catcher Austin Bossart, who the Phillies selected in the 14th round, has agreed to a $5,000 bonus. Phillies general manager Ruben Amaro Jr.'s nephew, Andrew, who was picked in the 35th round, agreed to a $1,000 bonus.
Deals could be announced as early as Tuesday, assuming those players pass their physicals.
Todd Zolecki is a reporter for MLB.com. Read his Phillies blog The Zo Zone, follow him on Twitter and listen to his podcast. This story was not subject to the approval of Major League Baseball or its clubs.