* Alibaba offers $21 per ADR, a premium of 27 percent
* Deal allows Alibaba to increase relevance of maps to users
* Three-way mobile fight shaping up between Alibaba, Baidu, Tencent (Recasts to add details on strategy, adds comment)
Feb 10 (Reuters) - Alibaba Group Holding Ltd, China's largest e-commerce firm, offered on Monday to buy AutoNavi Holdings Ltd in a deal valuing the Chinese digital mapping and navigation firm at $1.58 billion.
Alibaba, which already owns 28 percent of AutoNavi, is expanding its product offerings to better compete with rivals Tencent Holdings Ltd and Baidu Inc, as China's biggest Internet firms continue to chase growth by buying online businesses.
Revenues at AutoNavi have declined sharply over the past three quarters and Alibaba's move is expected to protect its initial investment in the Beijing-based firm. Given Alibaba's 28 percent stake now, it is expected to pay between $1.13 and $1.17 billion for the remainder.
AutoNavi's mapping technology could help Alibaba grow revenues from bricks and mortar stores while gaining greater control over product development at one of China's dominant mapping companies.
"What it enables Alibaba greater access to is technology and insight into the mapping sector. Full control would grant more control over design and product for AutoNavi's products and services," said a source familiar with the matter.
Alibaba would be better able to integrate its own "point of interest" data into maps to make them more relevant to users, said the source, such as customer reviews of shops and restaurants and paying for goods before arriving at a shop.
As of the third quarter in 2013, AutoNavi was the leading mobile map service by users, according to Beijing-based Analysys, with 31.3 percent of the market, followed by Baidu with 26.6 percent.
As of December, 81 percent of all Internet users in China go online with mobile devices, according to the official China Internet Network and Information Center.
Alibaba, video game and social network cash cow Tencent and search giant Baidu, have all aggressively invested in developing and acquiring businesses that can cash in on the explosion in smartphone and tablet use.
These investments include social networks such as Tencent's Weixin, known overseas as WeChat, and Sina Corp's Sina Weibo, a micro-blogging platform in which Alibaba bought an 18 percent stake in April last year.
Alibaba is expected to go public later this year in the largest IPO since Facebook Inc's debut in 2012, although the firm has not chosen a location.
Alibaba has been valued at around $140 billion, according to a Reuters poll of eight analysts.
A key battleground for these companies is what is known in China as "online-to-offline" (O2O), turning something like a search query on a smartphone into a physical purchase in the real world.
An Alibaba AutoNavi acquisition would fit with the e-commerce company's bid to diversify online shopping away from the desktop and into handsets and shops.
Baidu started offering its map software for free last August, challenging AutoNavi for the Chinese navigation market. AutoNavi followed suit by offering its own navigation software for free.
"The market for navigation and map applications and services has become increasingly challenging," Alibaba said in a letter to AutoNavi, arguing that its proposal provided value that would be difficult for it to achieve on its own.
Alibaba and AutoNavi declined to comment beyond the filing to the U.S. Securities and Exchange Commission and AutoNavi's press release.
AutoNavi, which has not reported fourth-quarter results, posted year-on-year declines in revenue in each of the first three quarters of 2013. Revenue for the first three quarters totaled about $110 million.
More than half of AutoNavi's revenue comes from licensing map data for dashboard navigation systems used in cars. Customers include Audi, BMW and General Motors Co.
AutoNavi, which went public in 2010, also provides map software for Samsung Electronics Co Ltd's smartphones as well as services to China Mobile Ltd and Google Inc.
AutoNavi said on Monday that Alibaba had offered to buy the 72 percent of the company that it did not own for $21 per American depository share, or $5.25 in cash per ordinary share.
The offer represents a premium of 27 percent to AutoNavi's ADR close of $16.54 on the Nasdaq on Friday. AutoNavi shares leapt 24.4 percent by close of trading on Monday.
The company's shares have risen about 47 percent in the past year. The stock was trading at 39 times earnings for the last four quarters, more than double that of other navigation device makers such as Garmin Ltd and TomTom NV.
Alibaba, which is 24 percent-owned by Yahoo Inc, announced its 28 percent stake in AutoNavi in May.
AutoNavi said it would form a committee including financial and legal advisers to consider the offer, which Alibaba plans to fund with cash on hand.
Alibaba runs Taobao Marketplace, China's largest consumer-focused e-commerce website; Tmall.com, a business-to-consumer site often compared to Amazon.com Inc ; and Alipay, a PayPal-like online payment platform affiliated with Alibaba.
(Reporting by Sampad Patnaik and Chandni Doulatramani in BANGALORE and Paul Carsten in BEIJING; Editing by Saumyadeb Chakrabarty and Matt Driskill)