The WikiLeaks claim follows the latest emails it disclosed from a hack of Democratic presidential nominee Hillary Clinton campaign chairman John Podesta's emails, the BBC reported.
It released three transcripts on Saturday of Clinton's paid speeches to Goldman Sachs, which her campaign had long refused to release.
The tweet further said the group had "activated the appropriate contingency plans".
Assange has been claiming asylum at London's Ecuadorean embassy since 2012 to avoid extradition over sex assault allegations in Sweden.
The Ecuadorian government has not responded to the claims, the Guardian reported.
"We don't respond to speculation circulating on Twitter. Ecuador will continue to protect Julian Assange and uphold the political asylum granted to him in 2012," a source in the Ecuadorian government said.