A visit by Albayrak, son-in-law of Turkish President Recep Tayyip Erdogan and a key member of his inner circle, would be a significant diplomatic move by Ankara after a rapprochement deal last year between the two countries mended a long-standing rift.
The crisis was triggered by Israel's deadly storming in 2010 of a Gaza-bound ship which left 10 Turkish activists dead. But the two countries normalised ties in June last year and rapidly begun discussing the gas pipeline project.
"Hopefully, Mr. Albayrak will pay a visit to Israel this year in 2017, which will help us accelerate and try to conclude this agreement," the minister said at the World Petroleum Congress in Istanbul after meeting Albayrak.
He added that no exact date had been fixed but it would take place in the coming months.
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Turkey, which largely depends on foreign supplies for its energy needs, is keen to diversify resources and has a close eye on Israel's own developing resources.
"We want to build a pipeline stretching from Israel to Turkey in order to able to export natural gas from Israel to Turkey," Steinitz said, adding that the Israeli gas could be delivered to Europe and to the Balkans through Turkey.
Israel is also moving ahead with plans, together with Italy, Greece and Cyprus, to build the world's longest undersea gas pipeline from the eastern Mediterranean to southern Europe, with support from the European Union.
If carried out as planned, the long-discussed USD 6.2- billion pipeline will take gas from Israel and Cyprus's offshore gas reserves to Europe, potentially reducing European dependence on Russian energy.
Erdogan warned this week global energy companies to stay away from any deal with Cyprus for gas and oil exploration in the eastern Mediterranean after talks missed a "big opportunity" to unite the divided island.
Asked if eastern Mediterranean could be a source of tension between Israel and Turkey, Steinitz said: "Hopefully this region will find its way in the future to cooperate and establish good relations," he said.