Haniya is expected to remain in the Gaza Strip, the Palestinian enclave run by Hamas since 2007, unlike Meshaal who lives in exile in Doha and has completed the maximum two terms in office.
The Gaza-based resistance group held elections on Saturday to elect a new political bureau chief to replace Khaled Meshaal.
The polls were held in the Gaza Strip and Qatar's capital Doha simultaneously via video conference, a source said on condition of anonymity because he was unauthorized to speak to media.
The top contenders included former prime minister Ismail Haniyeh and senior Hamas leaders Moussa Abu Marzouk and Mohammed Nazzal.
Haniyeh and other Hamas leaders were scheduled to leave for Qatar to participate in the vote, but the closure of the Rafah crossing between Gaza and Egypt prevented them from travelling.
Meshaal was elected Hamas leader in 1996.