According to the al-Bayan newspaper, senior Hamas members claim the deal requires the group to dismantle its military wing and stop all aggression against Israel, in exchange for the U.S. and E.U. removing Hamas's name from the international list of terror organizations.
He said the group has not yet rejected the proposal and is presently examining what the offer entails.
'A moderate Islamic movement'
In addition, he renounced reports that dialogue between Hamas and the U.S. has begun, but did not rebuff rumors that it may occur in the future.
"In the end, we are not the Taliban, al-Qaeda or even Iran who determine borders for its citizens in the name of Islam," he said. "We are Hamas - a moderate Islamic movement."
He said the group's military wing would exist as long as the occupation continues.
"Once you solve the Palestinian problem and the occupation will come to an end, our military wing will cease to exist," he said. "We believe the Jihad is a means and not an aim.
He said there is noting preventing Hamas from recognizing Israel and accepting the idea of two states living side-by-side, as long as Israel retreats to its 1967 borders.
This is not the first time the media has reported possible talks between Hamas and U.S. and Europe officials. Two United Arab Emirates newspapers reported on Saturday that senior Hamas and Hizbullah members both received official letters from the U.S administration and British government.