"The Clintons' tentacles go everywhere," Jordan told the Hill.
Downer, Australia's High Commissioner to the UK, first emerged as an important figure in the Russian meddling controversy late last year.
The New York Times reported former Trump foreign policy adviser George Papadopoulos told Downer during "a night of heavy drinking" in London in May 2016 that Russia had political dirt on Hillary Clinton.
Downer passed the information to Australian intelligence officials who forwarded it to their US counterparts. It led the FBI to open an investigation in July 2016 into Russia's attempts to disrupt the presidential election.
Republican members of congress are concerned that Downer's connection to the Clinton Foundation confirmed nearly all of the early evidence the FBI used to justify its investigation into Trump came from Clinton supporters, including the dossier compiled by former British intelligence officer Christopher Steele.
Hillary Clinton's spokesman, Nick Merrill, slammed the effort to link Downer and the 2006 grant to the Russia probe.
"The idea that this has anything to do with his government deciding a decade earlier to partner on HIV/Aids work with the Clinton Foundation, or the fact that as a United Nations envoy, he met with Secretary Clinton at the State Department, is laughable," Merrill told the Hill.
Adam Schiff, the top Democrat on the US House Intelligence panel, defended Australia.
"Not content to disparage our British allies and one of their former intelligence officers, the majority now seeks to defame our Australian partners as a way of undermining the Russia probe," Schiff said.
Australia's Department of Foreign Affairs and Trade issued a statement defending the grant and its "strong outcomes" in fighting HIV-Aids.
"The funding provided to the Clinton Foundation and its affiliate was used solely for agreed development projects," DFAT said.
- AAP