Urbon said Friday that an Internet report that indicated the 30-year-old Fukudome was headed to the United States to play in the Major Leagues next season was incorrect.
"He's not going to decide until Tuesday, or Monday our time," Urbon said. "If he had made that decision, you would have seen it out of Japan by now."
Urbon said Fukudome -- who has been made a generous offer by the San Diego Padres and the Chicago Cubs and possibly a third team -- is still mulling over an offer by the Yomiuri Giants and would not make a decision to leave Japan without informing the Giants of that decision.
"That would be culturally very disrespectful to make that decision," Urbon said.
The Padres have made Fukudome an offer believed to be four years and less than the $52 million extension pitcher Jake Peavy agreed to earlier this week.
San Diego CEO Sandy Alderson told the Associated Press late Thursday that the offer was "one of the two or three biggest deals" in franchise history.
"We didn't make a $60 million or $50 million offer," Alderson said.
Urbon said all the offers from Major League teams have been sent to him, and "we've communicated the details of the offers to Kosuke. He's got enough information to decide which [offer] he plans on taking early next week, the Tokyo [Yomiuri] offer or a Major League club."
"I'm crossing my fingers the he comes," Urbon said. "If he does decide to come, it will [accepting an offer] likely happen quickly."
Corey Brock is a reporter for MLB.com. This story was not subject to the approval of Major League Baseball or its clubs.