Speaking to the Financial Times, Neumann said the budget sector was "very interesting," and confirmed the brand was "definitely looking at the segment."
The plan involves bringing in two new low-cost models to plug the gap left by Chevrolet, which will be axed from the European market next year.
One of the cars has already been spotted testing, and is likely to be badged as Viva when it makes its debut at the Geneva motor show in March next year.
Sitting alongside the Adam and below the new Corsa in size, the car is based on the next-generation Chevrolet Spark, but likely won't be priced to compete with the £5995 Dacia Sandero. Instead, Vauxhall is understood to be pitching the new model towards the Ford Ka, which costs from £8945.
"We think there is possibility for Opel to come up with some entry-level product, specifically now Chevrolet is out of the market," said Neumann. "We had Chevrolet, which looked like a budget brand, but it was not."
Neumann also confirmed that GM is eyeing up a compact crossover to sit alongside the new Viva in its budget line-up. That model is likely to be pitched against the Dacia Duster, and could well form the basis of a replacement for the current Meriva MPV.
In the first six months of this year, Dacia's sales in Europe have risen by more than 36 per cent, to 192,876 units, with 37,802 cars sold in June alone. GM's sales – incorporating the Opel/Vauxhall and Chevrolet brands – are down by 0.5 per cent in the first half of 2014, selling a total of 497,143 cars.