If they clear by noon on Tuesday, they both could be sent to the AHL's Lehigh Valley Phantoms.
To get their roster to 23 players, the Flyers need to send at least one player to the Phantoms by Tuesday's 5 p.m. deadline.
Because of his team-friendly contract ($720,000) and his youth, the 24-year-old Leier may be picked up by another team. Leier can provide speed and penalty killing for a team in need.
Weise, 30, has two years left on his contract, one that has an annual cap hit of $2.35 million.
The moves mean veteran Jori Lehtera, who had been on the roster bubble, will be with the team at the start of the season.