Abubakar has not formally left the ruling People's Democratic Party (PDP), but his allies have set up a factional headquarters and issued statements using PDP letterheads.
"The president could declare the vice-president's position vacant, but that would be another sign of lawlessness," said a senior PDP member, adding that due process required that Obasanjo seek a court ruling before taking any action.
"The president has the use of the police, so he could give Atiku seven days to leave and he could implement it," he added.
End of a dictatorship
Garba Shehu, a spokesperson for Abubakar, said such a declaration would be unconstitutional.
"If some people want to act outside the law, that would be a coup d'etat. It means someone has overthrown the constitution.
"We don't have police or army so we can't fight back but we will go to the courts," he said.
Obasanjo's election in 1999 marked the end of three decades of almost continuous army dictatorship, but politics are still characterised by bribery, violence and vote-rigging.
A US-based political analyst said the confusion caused by any questionable removal of Abubakar could encourage the military to return.
"Unless cooler heads prevail, the country's political system could careen into a constitutional crisis with two vice-presidents by week's end and maybe tempt the military back into politics," said Sebastian Spio-Garbrah, Eurasia Group analyst.
Obasanjo's choice to lead the PDP into elections is Umaru Yar'Adua, who is a little-known governor from Katsina State.
Critics say Obasanjo chose the reclusive former teacher with a kidney condition because he wants to run the next government by remote control and ensure protection from prosecution in the wake of the sleaze allegations made by his deputy.
The Action Congress, last week signed an alliance with the main opposition All Nigeria People's Party (ANPP) under which the two parties agreed to field a single presidential candidate for the elections.
Former military ruler Muhammadu Buhari won the ANPP ticket on Monday, and now the parties will have to choose between two heavyweights of Nigerian politics.
Buhari's government, which lasted from 1984 to 1985, was famous for draconian austerity measures, is wildly popular among the masses in northern Nigeria but he has limited funds.