Speaking in Parliament on Tuesday, the Belgian MEP said his group, the fourth biggest in the institution, had "no set position" on its preference for the presidency.
His comments come amid growing speculation that current President, German MEP Martin Schulz, will seek to continue in the post beyond January 2017, when he was supposed to step down as part of a deal between the EPP and S&D groups.
Some, including Socialist leader Gianni Pittella and Commission President Jean-Claude Juncker, are believed to support his continued presidency.
There is opposition to all three EU presidencies being held by centre-right politicians; Council President Donald Tusk and Juncker are both EPP members.
But others, including the EPP, want a new President to complete the second half of the current legislative term.
At a news conference in Strasbourg, Verhofstadt said, "We have no set position on this yet. Other groups appear to be coming to quick and hasty decisions, but I'd rather look at the substance of this rather than the personalities."
His group, he said, would debate the issue at an upcoming meeting in Prague.
Other candidates touted for the post include French EPP group deputy Alain Lamassoure, Irish centre-right member Mairead McGuinness, and former European Commissioner Antonio Tajani.
Schulz was the first president of parliament ever to be re-elected for a second term in July 2014.
Speaking separately on Tuesday, EPP group leader Manfred Weber said, "The presidency is not decided until January and that is a long way off. It is important we give ourselves time to discuss this. We will do that as and when."