Speaking at a news conference in Strasbourg on Tuesday, the Belgian deputy gave a strong signal that he will make a last minute entry into the race for Parliament's top job.
He told reporters, "I will make an announcement about my candidacy in the next few days."
He pointed out that the successful candidate will need an absolute majority in a secret ballot of MEPs in January and suggested that those who have so far declared their candidacies may find it difficult to command such a majority.
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Verhofstadt, a former Prime Minister of Belgium, is also Parliament's chief negotiator in the upcoming Brexit talks.
The presidency has become vacant after Schulz decided to return to German domestic politics.
Meanwhile, EPP group Chair Manfred Weber has indicated that he will not stand for the presidency.
His group, the biggest in Parliament, will select its nominee at what Weber said will be a "very lively" meeting on Tuesday evening.
The EPP group candidates are Alain Lamassoure, a former French EU affairs minister, Alojz Peterle, a member from Slovenia, Mairead McGuinness, a Vice-President of Parliament from Ireland, and Antonio Tajani, an Italian deputy and former European Commissioner.
Weber said that as the biggest group - the EPP has 216 members - it has the "right" to the presidency for the second half of the current mandate. Schulz, a Socialist, held it for the first half.
He said that as an EPP President would come from the biggest group he or she would "represent the whole institution."
Socialist leader Gianni Pittella is the nominee from his group, which insists that all three of the EU presidencies - Parliament, Commission and Council - cannot be held by people from the EPP family at the same time.
Weber revealed that he had urged his group to support a continued Schulz presidency, although this had been overtaken by Schulz's decision to quit Parliament.
He said, "Schulz has made a top contribution and achieved a lot for this Parliament in his term but we now need to usher in a new chapter."
The German described all four EPP nominees as "strong candidates" with "different backgrounds and histories.
"It is good that all EPP members have the right to make a choice. The selection today will be done in an open and transparent way."
On the so called grand coalition with the Socialists, he said, "We want to reach an agreement with other groups but we now have a series of candidates vying for the presidency and, as the biggest group, we are entitled to this for the remainder of this mandate."
Further comment came from Greens co-Chair Philippe Lamberts who said, "While it is very unlikely the next President will be from our group we hope to sway opinion on this.
"We are profoundly dissatisfied with the way Schulz has done his job as President so we are hoping there will be major changes in the next two and a half years.
"Even so, I find it hard to believe that, as has been claimed by the Socialists, the grand coalition is over."