The Liberal Party will examine the record of Greens candidate Alex Bhathal, looking for links to any "anti-Semitic" activity before deciding to put up a candidate in the looming Batman by-election in Melbourne's inner-north.

Liberal Victorian state president Michael Kroger said he wanted the party to field candidates against Greens who had been involved in protests and campaigns against Israel's treatment of Palestinians. Mr Kroger regards such protests as anti-Semitic activity.

Labor's David Feeney, who resigned on Thursday, defeated Ms Bhathal in the 2016 election in Batman only with the help of preferences from the Liberals and the party's intentions for the looming byelection have been the subject of intense speculation since Mr Feeney announced his decision.

The Liberals didn't put up a candidate in last year's byelection in the state seat of Northcote, which lies wholly within the federal Batman electorate.