* Pipeline would let EU export more Russian gas back to Ukraine
* Deal could help bring about historic Ukraine-EU pact
* Slovakia link would add to Hungarian and Polish reverse flows
(Updates with Ukrainian confirmation, adds background)
BRUSSELS, Nov 19 (Reuters) - Pipeline operators in Ukraine and Slovakia are on the verge of signing a deal that will allow the European Union to ship gas through Slovakia to Ukraine, reducing Kiev's dependence on Russia, the European Commission and Ukraine said on Tuesday.
The pipeline flow agreement could also help to bring about a historic partnership agreement between the EU and Ukraine, which both Russia and the EU are vying to tie into their respective spheres of influence.
Asked whether a deal was about to be signed, Ukraine's Fuel and Energy Minister Eduard Stavytsky told Reuters: "Yes, no doubt."
European Commission spokeswoman Marlene Holzner said: "We consider that we are very close to a deal ... The content of the deal has been agreed, whereby the gas will flow from West to East through Slovakia to Ukraine. It's just a matter of signing, which should be in the next few days."
The reverse flow deal should be the climax of more than a year of talks brokered by EU Energy Commissioner Guenther Oettinger.
The gas would be shipped by physical reverse flow, through existing, unused pipelines, plus a small section of pipeline to be built next year.
The EU has a keen interest in strengthening ties with Ukraine, whose gas price disputes with Russia's state-controlled Gazprom have disrupted supplies to both Ukraine and the EU. If Ukraine meets the EU's conditions, it looks likely to sign agreements on trade and other forms of cooperation with the EU in Vilnius on Nov. 29.
However, Russia has made very clear that it wants Ukraine to join a Russian-centred free trade zone with Belarus and Kazakhstan instead, saying it fears a loss of competitiveness for its goods.
The European Union for its part has been courting Ukraine with the idea it could become a gas hub, rather than just a transit state that depends on a dominant supplier: Russia.
Since late last year, technology allowing pipeline flows to be reversed has allowed Ukraine to re-import some Russian gas back from EU nations, notably from Hungary, and from Germany via Poland.
While Gazprom is far from happy about its gas being re-exported back to Ukraine, there is little it can do because EU law allows it, and Gazprom makes much of its reliability in never having broken a contract with the EU.
Reverse flow through Slovakia is more helpful to Ukraine because volumes would be higher.
But it is also politically sensitive in Slovakia, which is reluctant to annoy Russia, its main gas supplier, and wants to be certain that it will not be left short if a prolonged cold spell boosts demand and depletes reserves.
A spokesman for Slovakia's gas pipeline operator Eustream said late on Monday that Eustream was cooperating with its Ukrainian partners but could not disclose details until a deal was signed.
(Additional reporting by Martin Santa in Brussels, Pavel Polityuk in Kiev, Michael Kahn in Prague; Editing by Kevin Liffey)