Student activists at the University of Cape Town (UCT) who staged the "poo protest" want the statue torn down, calling it a symbol of white oppression.
They are planning a protest march on Friday after 10 days of mounting controversy over the faecal attack.
The university campus was built on land donated by Rhodes, a mining magnate and champion of British imperialism in the late 1800s, who gave his name to the former Rhodesia, now Zimbabwe.
But, he said, the decision had to be taken by the university council, and he proposed talks involving students and staff ahead of a council meeting on April 15.
"I do not think the statue should be destroyed or hidden away. I just think it should not be there -- it should be moved," he said in a statement.
The president of the Student Representative Council, Ramabina Mahapa, described the plan as "meaningless" and demanded immediate action.
Students have dismissed Rhodes' campus bequest as an argument against removing the statue, saying the land was stolen from black Africans in the first place.
Monuments to South Africa's racist white-minority rule are scattered throughout the country and are regular targets of protest.
But the discontent among some black university students goes beyond symbols to cover admission policies and the racial make-up of the teaching staff.
"University leaders make a strategic mistake to think these protests are simply about statues," said the vice-chancellor of the University of the Free State, Jonathan Jansen.
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