Players underwent physicals on Monday before the team's minicamp begins Tuesday.
Ballard is recovering from a torn ACL and microfracture knee surgery and could miss the entire season. A source said Ballard is expected to return once he clears waivers and be placed on either the physically unable to perform list or injured reserve. Ballard and his agent, Blake Baratz, both said on Twitter that the tight end will return to the Giants if he clears waivers.
"Thanks for love everyone but don't worry, its a business, I'm on the road to recovery, and I believe I'll be in a Giants uniform in '13," Ballard wrote.
The Giants like the 6-foot-6 Ballard, who had a breakout season last year with 38 receptions for 604 yards and four touchdowns in 14 games.
Ballard, who emerged as a starter in 2011 despite not being drafted out of Ohio State, suffered a knee injury during Super Bowl XLVI and attempted to return to the game by testing his knee on the sideline before crumpling to the turf in pain.
The Giants lost two tight ends -- Ballard and Travis Beckum -- to torn ACL injuries in their Super Bowl win over the New England Patriots. While Beckum optimistically hopes to return around the start of the season, Ballard has said all offseason that it's possible he could miss the season. Ballard was hopeful that he could return by mid-season. The Giants signed free agent Martellus Bennett and drafted tight end Adrien Robinson in April.
Bernard is entering his 11th season and had 30 tackles. Bernard, who also had a sack during the Giants' postseason run, adds more depth to a defensive line that includes Chris Canty, Linval Joseph, Shaun Rogers and Marvin Austin at defensive tackle.