"The decision has already been made at Milan headquarters....Eni is abandoning Polish shale gas," the Puls Biznesu daily said, citing anonymous sources.
Eni did not immediately respond to a request by news agency AFP for comment.
Poland, one of Europe's leaders on shale gas, has made tapping its deposits a priority in the hopes that it will ensure energy independence from Soviet-era master Moscow.
The European Union member currently imports about two-thirds of the 14 million cubic metres of natural gas it uses annually from Russia.
Poland's shale gas reserves are estimated at between 800 and 2,000 billion cubic metres.
But the shale sector has suffered a string of setbacks, as global energy groups Exxon Mobil, Marathon Oil and Talisman Energy have scrapped Polish shale gas exploration.
These firms "did not find the shale gas deposits they expected," sector expert Andrzej Szczesniak said.
Eni has three concessions in Poland, of which one has already expired and the others are due to expire soon. The firm will not seek to renew them, according to Puls Biznesu's report.
Anna Miazga, a government mediator between supporters and opponents of shale gas, said that Eni's concession in the northern town of Mlynary expired on January 5th.
"Eni informed us that they would no longer take part in a local dialogue with residents because the group decided to not renew its Mlynary concession," she said.
Various international firms have already drilled several dozen test wells, but it will take around 350 such wells to determine the profitability of commercial exploitation.
The Polish government plans to invest €12.5 billion by 2020 in the shale gas sector.