By Paul Sandle and Sophie Sassard

LONDON (Reuters) - Vodafone faces a battle for Germany's largest cable company, Kabel Deutschland, although rival bidder Liberty Global of the United States has bigger regulatory and funding hurdles to overcome.

Liberty Global, which owns Unity Media, Germany's second biggest cable operator, joined the race on Tuesday. It tabled an 85 euro a share offer, according to a person familiar with the matter, days after the British mobile company said it was in talks about a deal.

Vodafone wants to buy the cable company so that it can offer TV, fixed line and broadband to more of its mobile customers, while Liberty Global wants more consolidation in one of its best performing markets. Vodafone offered about 81-82 euros a share in cash, sources said last week.

Shares in Kabel Deutschland were trading 3.8 percent higher at 85.6 euros by 1010 GMT, valuing the group's equity at 7.56 billion euros ($10.1 billion).

A Liberty Global deal would be closely scrutinized by German anti-trust authorities, a hurdle recognized by Liberty Global's chief financial officer Charles Bracken last week.

He told a Goldman Sachs cable conference on June 12 that while the industrial logic for consolidation in Germany was compelling, regulatory opposition remained a significant barrier to any deal in the near future, the bank said in a note.

Germany's competition regulator in February blocked Kabel Deutschland's bid to take over smaller Berlin-based cable group Telecolumbus for 618 million euros.

A source familiar with the situation said Liberty has already talked to German antitrust office to discuss the deal, but declined to elaborate.

Liberty Global customers in Germany are in the densely populated German state of North Rhine-Westphalia as well as in Hesse and Baden-Wuerttemberg, while Kabel Deutschland is active in the rest of Germany.

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Vodafone and Liberty face battle for Kabel Deutschland