The British cleric, who is beginning a nine-day pastoral visit to central Africa, has asked for a meeting with Mugabe amid reports of violence between rival factions of Anglicans, the British broadcaster said.
Anglicans in the country have been divided since 2007 when the former bishop of Harare, Nolbert Kunonga, separated from the Anglican churches, complaining gay priests and church members had too much influence.
Williams expelled Kunonga, an ardent supporter of Mugabe, but courts in the country ruled Kunonga should retain control of church buildings in the capital.
The BBC said tear gas has been fired into churches loyal to Williams and worshipers have been beaten during services.
Kunonga has been accused by critics of using people loyal to Mugabe's Zanu PF party to carry out the attacks.
A spokeswoman for Williams said he hopes to "show solidarity" with fellow Anglicans and their bishops, who he said served their communities in the face of "disruption, intimidation and even violence."
During his visit to Zimbabwe, Williams is to preach at the National Sports Stadium in Harare and visit programs that care for orphans and human immunodeficiency virus sufferers.
His visit starts in Malawi, where Williams will celebrate the 150th anniversary of its Anglican branch.