* Fortum in talks to buy E.ON stake for 3.8 bln euros
* Deal would trigger offer for rest of Uniper
* Uniper says offer "clearly not in line" with its strategy (Adds comments from Fortum, Uniper and analyst, updates shares)
FRANKFURT/HELSINKI, Sept 20 (Reuters) - Finnish power company Fortum is in advanced talks to buy for 3.8 billion euros ($4.6 billion) German utility E.ON's remaining stake in Uniper, the power stations and trading business it spun off last year.
The news in statements by both Fortum and E.ON on Wednesday was greeted with dismay by Uniper, which some analysts said could be broken up by Fortum.
State-controlled Fortum is focused on carbon-free power generation, mainly in the Nordic region and Russia, and has been looking for a deal since selling its power distribution grids for 9.3 billion euros in 2014 and 2015.
Sources close to the matter told Reuters that Fortum was mainly interested in Uniper's hydropower plants and interests in Swedish nuclear power stations, and it was already working with a partner that might take on Uniper's coal-fired plants.
"This (announcement) shows there were no optimal deals on the market for Fortum," said Inderes Equity Research analyst Petri Gostowski, who has a "reduce" rating on Fortum shares.
Fortum said it was offering 22 euros a share for E.ON's 46.65 percent stake in Uniper.
Under German takeover rules, it will have to make an offer for the rest of Uniper's shares if the deal goes through.
Fortum said it would launch a voluntary offer in early 2018, but that it was only focused on E.ON's stake and intended to be a constructive partner to Uniper.
"This is not a takeover, it's a significant investment," Fortum Chief Executive Pekka Lundmark told a conference call.
"We expect that there will be very interesting cooperation possibilities between the two companies."
The potential bid values Uniper at 8.05 billion euros excluding debt, a 4.5 percent premium to Tuesday's closing price and a 36 percent premium to the share price in May, before talk surfaced of a potential deal.
Uniper shares were up 5.8 percent to 22.26 euros at 1415 GMT, signalling investors are hopeful of a higher bid, while Fortum's stock was up 4 percent and E.ON's up 3 percent.
Asked whether Fortum could sweeten its offer, Lundmark said: "This is very simple. This is the only offer there is."
Uniper was taken aback by the announcements.
"This unsolicited takeover offer is clearly not in line with the strategy of Uniper," its chief executive, Klaus Schaefer, said in a statement.
Uniper, with total sales of around 67 billion euros in 2016, operates roughly 40 gigawatts of power plants in Europe and Russia. It has hydroelectric, coal- and gas-fired plants as well as stakes in gas pipelines, liquefied natural gas terminals and nuclear plants across Europe, plus energy trading operations.
Over the summer, Fortum proposed a full combination of the companies, but Uniper was not interested, Lundmark said.
A deal would not change Fortum's clean energy vision, he added.
"We believe that this transaction would be able to speed up the European energy transition ... it is about decarbonisation, which is extremely important," he said.
Plagued by years of falling wholesale power prices, E.ON spun off Uniper to focus on its renewable energy and grids businesses.
In May, E.ON said it planned to sell its remaining stake in Uniper soon, with options including a market placing or a sale to a third party. However, it cannot complete a deal on Uniper before next year without incurring a large tax bill.
Last month, Uniper raised its dividend and profit forecast for 2017, pushing its share price to the highest since its market debut in September 2016.
($1 = 0.8331 euros)
(Additional reporting by Vera Eckert and Tuomas Forsell; Editing by Greg Mahlich and Mark Potter)