However, Abu Mujahid, a spokesman for the Popular Resistance Committees, said the soldier could be harmed by Israel’s military activity.
"Gilad Shalit’s life is in danger through the incursion and bombing of houses," said Abu Mujahid.
Shalit was captured in a June 25 cross-border raid by militants from the Popular Resistance Committee, a violent group with ties to the ruling Hamas movement.
Israel invaded Gaza shortly after the kidnapping. Last week, it stepped up its operations in the northern Gaza Strip, aiming to halt Palestinian rocket attacks.
Nearly 50 Palestinians, most of them terrorists, have been killed since last Wednesday.
Egypt has been trying to mediate a deal in which Israel would free dozens of Palestinian prisoners in exchange for Shalit. But the sides have not been able to reach a solution.