"This union could start with two or three" members of the Gulf Cooperation Council, she told AFP, adding that the proposal for a Gulf union put forward by Saudi King Abdullah was "backed by Bahrain."
Unlike most other Gulf countries ruled by Sunni dynasties, Bahrain was hit last year by a wave of protests inspired by the Arab Spring and led by its Shiite majority.
The tiny neighbour of the Gulf heavyweight continues to see frequent confrontations between police and protesters despite a brutal crackdown on mass protests in mid-March last year, a day after Saudi forces rolled into Bahrain to help quell the uprising.
On Friday, a top Gulf official who requested not to be named also said Gulf leaders will "discuss the idea of a union between Saudi Arabia and Bahrain."
Rajab declined to elaborate on the nature of the proposed union, saying only that it could follow the "European Union model."
"In Bahrain, we support setting up a Gulf union to protect us from the threats facing the region on the political, economic, security and military fronts," she said.
King Abdullah told his fellow Gulf leaders in December that the GCC should move from the "phase of cooperation to a phase of union within a single entity."
A joint committee comprising three representatives of each member state is tasked with thinking the proposal through and should present its findings to Monday's summit."The idea of a Gulf union will be on the agenda of the summit in Riyadh" on Monday, said Samira Rajab.