One of Assange's lawyers welcomed the offer saying it would be a first step in clearing his client who has been holed up in the Ecuadorean embassy in London since 2012.
"He will accept" to be questioned in London, attorney Per Samuelsson told AFP, adding that his client was "happy" about the breakthrough.
"We are cooperating with the investigation," he said.
Up to now, Swedish prosecutors have refused to go to London to question Assange over the allegations.
But on Friday, the prosecutor in charge of the case said she was changing her stance as the statute of limitations on some of the alleged crimes will become effective in August.
"Marianne Ny has today made a request to Julian Assange's legal representatives whether Assange would consent to being interviewed in London and have his DNA taken via a swab," her office said in a statement.
"My view has always been that to perform an interview with him at the Ecuadorian embassy in London would lower the quality of the interview, and that he would need to be present in Sweden in any case should there be a trial," Ny said.
"This assessment remains unchanged," she said. But "now that time is of the essence, I have viewed it therefore necessary to accept such deficiencies to the investigation and likewise take the risk that the interview does not move the case forward," she said.
Sweden issued an arrest warrant for Assange in 2010 over charges made by two women of rape and molestation, AFP reported.
A lawyer for one of the women who has levelled the accusations against the WikiLeaks founder welcomed the prosecutors' offer.