Robert Mugabe broached the idea of sharing the Home Ministry, the official said, but the opposition has insisted on control of the police to restore the rule of law and to protect its supporters from state-sponsored attacks.
Opposition leader Morgan Tsvangirai expressed pessimism on Wednesday about talks on Zimbabwe’s proposed government of national unity.
A second day of talks between Tsvangirai and President Robert Mugabe ended in the early evening and will resume on Thursday.
"The proceedings have been quite circuitous," Tsvangirai told reporters outside the Harare hotel were the talks are being held.
A power-sharing agreement reached one month ago appears to be in danger of collapse because Mugabe’s party has laid claim to all the key ministries.
Tsvangirai, who is prime minister-designate, threatened over the weekend to walk out if the opposition party was only given minor posts.
Former South African president Thabo Mbeki is mediating the talks.