He said the Southern African Development Community and former South African President Thabo Mbeki had failed to resolve the stalemate.
The movement also called on SADC to withdraw from the negotiations.
An aide to Mr Tsvangirai, Mr George Sibotshiwe, who spoke to the media while in Kenya en route to Botswana said that the Movement for Democratic Change had no confidence in the role of SADC in the talks.
The MDC leader and his close associates are living in exile in Botswana. The negotiations between Mr Tsvangirai and President Mugabe have stalled after they failed to agree on the sharing of key Cabinet positions, especially those handling security.
MDC also said it did not want acting South African President Kgalema Motlanthe to take over the talks because his predecessor had failed.
However, it is understood that President Kikwete told the MDC leader that AU can only assume the responsibility after a resolution by its top organs and further consultations.
Mr Tsvangirai also met Prime Minister Raila Odinga in Nairobi on Wednesday night. It is understood that Mr Odinga backed his proposal that AU takes over the negotiations.
Mr Odinga said Africa was dragging its feet on the Zimbabwe crisis as its citizens continued to suffer because of poor leadership.
Later, while speaking to the BBC, Mr Odinga called on African leaders to take decisive steps to remove President Mugabe from power.
“Decisions have to be taken by African countries on Zimbabwe… and push him (President Mugabe) from power,” he said.
Meanwhile, African National Congress president Jacob Zuma met Mr Odinga on Tuesday night.
Mr Zuma met the Premier and other ODM leaders Musalia Mudavadi, William Ruto, James Orengo and Henry Kosgey during a stop-over at the Jomo Kenyatta International Airport.
Those privy to the meeting said Mr Odinga briefed Mr Zuma on progress of the Grand Coalition. SOURCE: The Daily Nation