The federal government could take an interest in the forthcoming Batman by-election if candidates appear to be anti-Semitic.
The Liberal Party could run a candidate in the Batman by-election if evidence is discovered that the Greens are anti-Semitic.
Victorian Liberals president Michael Kroger said his party had not ruled out running a candidate in the seat, which is being vacated by Labor MP David Feeney who was caught up in the citizenship fiasco.
"If we see a hint of anti-Semitism we will run," Mr Kroger told Sky News on Thursday.
He said an example of anti-Semitism was support within the Greens of the "boycott, divestment, sanctions" movement.
The BDS movement is seeking global support for an economic, cultural and academic boycott of Israel over its treatment of Palestinians.
Mr Kroger said the Liberals would prefer Labor to win the seat over an anti-Israel or pro-BDS Greens candidate.
The Liberal Party would conduct "research" into statements made, and events attended, by the Labor and Greens candidates before making its final decision, he said.