Hours later, police spokeswoman Vanessa Arlt said "we didn't find anything (to those reports) but we're still investigating in all directions and not excluding anything".
A security source added: "The scenario is such that an attack can not be ruled out".
An apartment elsewhere in the city has been searched by investigators. What makes this story take a freakish turn is that the driver of the vehicle shot and killed himself inside it.
Officials said a 51-year-old woman and a 65-year-old man were killed, while 20 others were injured.
Armin Laschet, the governor of North Rhine-Westphalia state where Munster is located, toured the city on Sunday.
The interior ministry said at least 30 people were injured.
Meanwhile, Herbert Raul, the state's interior minister, said that the driver of the van was "in all likelihood" a German-born lone attacker and not a refugee.
Authorities have said the attacker was a 48-year-old German citizen with mental health problems and that there was no indication of an Islamist militant connection. "The investigations are being conducted at full speed and on all fronts".More news: Boeing (NYSE:BA) Holdings Lifted by Cedar Capital LLC
Daniel Kollenberg, who witnessed the aftermath, told the BBC: "I think it is a deliberate attack because it's not allowed for cars to go in this area".
In a joint statement with police, prosecutor Martin Botzenhardt wrote Sunday that, "as of now, we don't have any leads regarding a possible background for the deed".
She said the man had three previous court procedures in Munster and one in nearby Arnsberg in 2015 and 2016.
On the other hand, the Associated Press reported that according to a police spokesperson, media reports on perpetrator having psychological issues too have not been confirmed.
Police also dispatched a bomb squad to the scene to check whether there were explosives in the van, the senior security official said.
The local daily Muenstersche Zeitung reported that the perpetrator had vaguely announced his suicide plans a week ago in an email to friends, but police would not confirm the details.
The Kiepenkerl is not only one of the city's best-known traditional pubs, but also the emblem of the city, depicting a traveling salesman with a long pipe in his mouth and a big backpack on his back.
The man killed two people when he ploughed the vehicle into people seated at tables outside the Grosser Kiepenkerl eatery, a popular destination for tourists in the old town of the university city in western Germany.