A Jordan spokeswoman, asked about the ultimatum, said the team had no announcements planned for Friday other than a report from testing in Barcelona.
Verstappen's website earlier quoted his management as demanding 'clarity' from the team by 1600 GMT.
"Jos Verstappen's management has officially confirmed that they and Trust manager Michel Perridon want clarity from Eddie Jordan this afternoon by 1700 hours at the latest about Jos' position within the Jordan F1 team," it said.
"They think that sufficient clarity has been created by both sides to reach a final decision," added the website.
"Jordan knows who Jos Verstappen is and also knows the input and wishes of the sponsors," it quoted management and Perridon as saying in a joint statement.
Jordan are the only Formula One team without any drivers announced for the 2004 season, which starts in Australia on March 7.
Germany's Nick Heidfeld, who raced for Sauber last season, was testing for the team in Barcelona on Friday and is the leading candidate for the drive if he can raise some sponsorship.
Britons Allan McNish and Ralph Firman, who made his debut with the team last year, are also in the frame.
Verstappen, a team mate of world champion Michael Schumacher at Benetton in 1994, has considerable backing but Jordan are his sole option after his management announced that he would not continue with his former team Minardi.