Tsvangirai and Mugabe signed a unity pact last September, but the agreement appears to be unravelling following a dispute over the control of key ministries and the abduction of several opposition and human rights activists.
Movement for Democratic Change (MDC) spokesman Nelson Chamisa told Reuters that the opposition party had sought a meeting with Mugabe on the dialogue.
"We have written to Mugabe, indicating that we want a meeting between him and (MDC) president Tsvangirai to bring finality and closure to the dialogue," he said.
"We cant keep Zimbabweans guessing, we have to close the chapter on dialogue, whether in success or failure."
Chamisa said Mugabe had yet to respond to the MDC’s overtures. He declined to give details on what Tsvangirai expected from the meeting.
Chamisa said Tsvangirai, who has been outside Zimbabwe since a regional summit in South Africa last November, would return to the country "within days".
Last week, Mugabe’s spokesman told state media the veteran leader would appoint a new cabinet in February, despite the stalled talks with the opposition. Chamisa said the MDC would not be part of that government.
Mugabe also fired nine ministers and three deputy ministers who lost their parliamentary seats in March polls and named acting ministers, in apparent preparation for the new cabinet.
"We have never stopped Mugabe from forming a fake and illegal government, but if he were to do that, he can be sure he will not have the support and co-operation of the MDC and the majority of Zimbabweans," Chamisa said.
"If they proceed, they would be in violation of the global political agreement and in defiance of SADC," he said, referring to the Southern African Development Community, a grouping of regional states which has been mediating between the two sides.
Chamisa said the MDC leadership had scheduled a meeting to discuss the deadlocked talks.
"The national executive council will meet on January 18 to assess the state of inter-party dialogue in the face of continued intransigence by ZANU-PF," Chamisa said.
"Depending on the factors at the time, critical positions will be taken, relating to the dialogue process."
Tsvangirai has threatened to pull out of negotiations following the abduction of several MDC and human rights activists.
Zimbabwe’s police have charged at least 16 activists of plotting an insurgency against Mugabe’s government.
Tsvangirai outpolled Mugabe in the first round of voting in March elections, but fell short of an outright victory to avoid a run-off poll won by Mugabe after Tsvangirai pulled out citing violence against his supporters.