Britain's Derek Warwick and Japan's Aguri Suzuki are the drivers for the team, who are ninth in this season's constructors' championship with only four points.
Jackie Oliver, a founder of the Arrows team taken over by Footwork three years ago, said: 'Footwork do not wish to continue footing the bill and they have asked us to find a substantial portion of the budget from somewhere else.'
But he stressed the company were not pulling out of Formula One. 'It is simply a case of the owners asking for support from outside,' he said. 'That is nothing new in Formula One.' Oliver added that he was confident the team would continue next season with some support from Footwork.
The group, based in Osaka and comprising about 50 companies, have reportedly spent three billion yen (pounds 19m) a year on the team.