Shurmur said he expects Beckham to attend the mandatory minicamp, which begins next Tuesday.
Beckham is recovering from a surgically repaired fractured ankle he sustained in Week 5 against the Los Angeles Chargers and has not attended seven of New York's 10 voluntary organized team activities. Monday was the fourth straight practice Beckham missed.
Beckham attended the team's first three OTAs and was also present at three days of voluntary minicamp before the 2018 NFL Draft.
The Giants have three more OTAs before the three-day mandatory minicamp on June 12-14. If Beckham does not appear, he can be fined approximately $70,000 under NFL rules.
So far, his practice time has been limited to individual running and catching drills.
Last week, Shurmur said Beckham was "pretty close" to getting full clearance from the doctors.
A three-time Pro Bowl selection, the 25-year-old Beckham was limited to four games in 2017 before getting hurt. Without their best offensive player, the Giants slumped to a 3-13 record last season while New York's offense ranked 31st in the league in scoring at 15.4 points per game.
Beckham has 313 catches for 4,424 yards with 38 touchdowns in four seasons with the Giants. He was named the 2014 Offensive Rookie of the Year.
Set to play for $8.5 million on the fifth-year option of his rookie deal in 2018, Beckham is seeking a long-term contract extension and a possible absence next week could be the precursor to a contract holdout when training camp starts in July.