The companies, which want to bulk up to better compete with the Netherlands' former telecoms monopoly KPN, offered concessions on July 12 but did not provide details.
The telecoms industry has seen a wave of consolidation in recent years as companies scale up to boost investments and take on bigger peers.
However, a tougher regulatory approach by European Competition Commissioner Margrethe Vestager since her appointment in November 2014, and demands for major concessions in return for her approval of merger deals, has worried the sector.
The merged company will be the second-largest telecoms company in the Netherlands. Liberty's Ziggo is the largest cable TV operator in the country, while Vodafone is the second-biggest mobile network operator.
The European Commission and Vodafone declined to comment. The EU competition authority is scheduled to decide on the deal by Aug. 3.
"We do not comment on speculation. We are in constructive dialogue with the European Commission and are confident of clearance in due course," a Liberty spokesman said.
Vodafone will pay 1 billion euros (£843.4 million) to U.S. billionaire John Malone's group to equalise their stakes in the merged company.
(Additional reporting by Kate Holton in London; Editing by Julia Fioretti and Mark Potter)
By Foo Yun Chee
