The comments by the former Belgian Prime Minister come after Trump's inauguration as the 45th US President.
Trump has already found himself embroiled in controversy about the size of the crowd for his swearing in on Friday and fresh attacks on the media.
Verhofstadt said, "The views of Donald Trump, and the hybrid war involving cyber-attacks and disinformation and political subversion being waged against the west by Russia, pose a profound threat to Brussels."
The Liberal deputy said, "It is increasingly clear that Trump and Russia now seek the disintegration of the European Union.
"Donald Trump admitted as much when he suggested that more countries would leave the Union following Britain's departure. What he really meant was: I hope they do. It is likely the new US President will nominate an ambassador to the EU who has only one quality - being a Brexit enthusiast.
"This is a remarkable turning point in the American approach towards Europe," said Verhofstadt.
His comments were slightly tempered by Anthony Gardner, the former US ambassador to the EU, who voiced "quiet optimism" in the team assembled by Trump to form the new administration.
Before stepping down last week, Gardner told this website, "I take some comfort in the nominees and that fact that they are mostly sophisticated people from the business community."
Many protests and marches took place around the world at the weekend, most notably the Women's March on Washington on Saturday. Thousands also gathered in Brussels on Friday for a Lights for Rights event, which was organised to coincide with the inauguration of Trump
Emma Woodford, one of the organisers of Lights for Rights, said, "We stand in solidarity with those marching in Washington and around the world. The politics of sexism and intolerance are not confined to the United States. Donald Trump's election is a symptom of this global affliction."
Co-organiser Tanja Gohlert added, "Many who never before considered themselves activists have been galvanised. We are united, ready to protect the rights of women and girls, and all who have been made to feel vulnerable."