* Offer could come as early as next week - source
* Indicative offer was 81 euros/shr - sources
* Kabel Deutschland rise to record 83.91 euros
* Vodafone declines to comment
FRANKFURT, June 14 (Reuters) - British mobile firm Vodafone is considering raising its offer for Kabel Deutschland after an initial 7.2 billion euro ($9.6 billion) bidwas knocked back by Germany's biggest cable operator, one personclose to the matter said.
"The offer could come as soon as next week," the person saidon Friday.
Vodafone declined to comment.
Vodafone sent a letter to Kabel Deutschland last weekannouncing its interest and indicating a price of 81 euros pershare, three people familiar with the matter have told Reuters.
Vodafone has confirmed that it made an offer to buy KabelDeutschland but has not provided details.
The world's second-biggest mobile operator has long beenlooking for its most important European market to meet growingdemand from customers for television, broadband, mobile andfixed-line services - so-called "quad play" - from one provider.
Any deal, which would be Vodafone's largest since 2007,could help it better compete against mobile operators, which arecutting prices, and against the pan-European cable group LibertyGlobal, which has been on an acquisition spree.
Vodafone had 32 million customers in Germany at the end ofMarch, making it the biggest mobile operator in the country.Kabel Deutschland is Germany's largest cable operator with about15 million of the 28 million homes passed by cable.
Kabel Deutschland shares were up 3.2 percent by 1320 GMTafter hitting another all-time high at 83.91 euros. Vodafoneshares were up 0.9 percent.
Vodafone (VOD)