Greek-Czech investment fund Emma Delta has been given until 1 May to submit an improved bid for Greek gambling monopoly OPAP.
According to a British Broadcasting Corporation report, its initial 622m euros ($812m; £526m) bid for a 33 per cent stake was rejected for being too low.
The fund has been urged to bid at least 650m euros, though the stock market values OPAP at just 726m euros.
Greece is obliged to raise 9.5bn euros from asset sales by 2016 under an international bailout plan.
In return, the European Union and the International Monetary Fund have committed to 240bn euros since 2010 in rescue loans for recession-hit Greece.
OPAP has a 10-year license to operate 35,000 video lottery terminals, as well as the exclusive rights to operate 13 games of chance until 2030.
Emma Delta said that there was nevertheless much “uncertainty over future revenue streams” and that it had identified “internal structural problems” at OPAP.