The party has proposed a range of policies to clamp down on immigrants in the Skåne region, including a total ban on immigration and to stop publicly funded integration programmes.
"Nobody would be forced to leave," Sten Andersson, leader of the Sweden Democrats on Malmö Council, told The Local.
The party, the fourth largest in Malmö politics, made the proposal in a submission to amend the council's budget.
"This would only apply to asylum seekers, not for instance to Danes who have been here for thirty years," he said.
Projects have previously existed through which immigrants who wanted to return to their countries of origin could get 30,000 kronor from the government to help them.
"Thirty thousand is not enough," said Andersson, "but we haven't put a precise figure on how these grants would be."
Andersson also wants to stop government grants for immigrant groups.
"We think that those who come to Sweden should be able to build whatever kind of Mosque they want, but they should pay for it themselves."
Other parties on the council have rejected the idea of paying immigrants to leave.
"A policy that creates a 'them' and an 'us' is nothing for us," said Daniel Persson, chief of staff for the ruling Social Democrats on Malmö Council.
"This is not a surprise coming from the Sweden Democrats. They have put forward these kinds of proposals before, but they have never got this kind of attention until now.
"There is unfortunately a breeding ground for political forces that do not support integration and for all people's equal worth. Fortunately there is a large majority on the council that supports a completely different kind of policy."