UPDATE 2-Finland's Fortum in talks to buy EO.N's remaining stake in Uniper

(Adds details, analyst, background)

FRANKFURT/HELSINKI, Sept 20 (Reuters) - Finland's 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 which it spun off last year.

Fortum said in a joint statement that it was offering to pay 22 euros a share for the 46.65 percent stake in Uniper and has not set a minimum acceptance threshold.

Shares in Uniper were up 6.6 percent at 22.21 euros at 1210 GMT, when Fortum's share price was up 6 percent at 17.21 euros and E.ON was up 3.4 percent at 9.50 euros.

Under Germany's takeover rules if Fortum strikes a deal with E.ON it would then have to make an offer for the rest of the company, which could be launched in early 2018.

E.ON cannot complete the deal to sell its Uniper shares before next year without incurring a large tax bill.

Given the lack of a substantial takeover premium for Uniper, the prospects of Fortum taking full control are unclear, a source close to the deal said, although Fortum is mainly interested in Uniper's hydropower plants and interests in Swedish nuclear power stations.

"As Fortum is happy for Uniper to be independent, we think they will be content even with a 51 percent ownership and will not sweeten the deal further," analysts at Bernstein said in a note to clients.

While Fortum could buy the whole company it is already working with a partner who may take on its coal-fired plants and other assets, another source close to the matter said.

"Fortum would focus on being an active, supportive and reliable shareholder of Uniper and a constructive strategic partner to Uniper, its management and employees," Fortum said.

The potential bid values Uniper at 8.05 billion euros excluding debt, a 4.5 percent premium to Tuesday's closing share price and a 36 percent premium to the share price in May, before a deal with Fortum was in prospect.

Uniper, with total sales of around 67 billion euros in 2016, operates hydroelectric, coal- and gas-fired plants and holds stakes in gas pipelines, LNG terminals and nuclear plants across Europe.

State-controlled Fortum, which is focused on Nordic and Russian markets, has been looking for mergers and acquisitions for years following its sale for 9.3 billion euros of its power distribution grids, but has so far announced only relatively small investments.

Last month, Uniper raised its dividend and profit forecast for 2017, pushing its share price to a record high since its market debut in September 2016.

Plagued by years of falling wholesale power prices, E.ON had spun off Uniper - which operates roughly 40 gigawatts of power plants in Europe and Russia - to focus on its renewable energy and grids business.

Wholesale prices have, however, picked up markedly from record lows set last year, with Germany's benchmark contract for delivery in 2018 up more than 40 percent over the past 12 months, partly driven by the closure of excess capacity across Europe.

E.ON Chief Executive Johannes Teyssen said in May the group planned to sell its remaining stake in Uniper soon, with options including a market placing or a sale to a third party.

($1 = 0.8331 euros)

(Additional reporting by Vera Eckert and Tuomas Forsell; Editing by Jason Neely, Greg Mahlich)