In a recent speech, Mr Blair said the simplistic solutions provided by nationalism which is advocated by Mr Salvini’s League could lead to a return to 1930s fascism.
The former prime minister even set up the Institute for Global Change to combat populism and its causes.
But now he is is going to discuss controversial plans to extend a gas pipeline from Azerbaijan to Puglia in southern Italy.
Italian Deputy Prime Minister and Lega Party leader, Mr Salvini, told Sputnik: “The TAP is an important strategic infrastructure for Italy and Europe: it is our intention to put it in place, obviously in consideration of every possible fallout it could have on the environment.”
Mr Blair has worked as a consultant on the Trans Adriatic Pipeline since 2014.
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It is also a pet project of Azerbaijan’s dictator, Ilham Aliyev.
But Mr Salvini said he is willing to hear from the former Labour Leader about the pipeline and other things.
Mr Blair did not offer any direct comment on the reason for the meeting.
The populist Italian coalition between the Five Star Movement (M5S) and the League is divided over the gas pipeline.
Mr Salvini said he would support the pipeline project and claimed it would help drive down gas prices in Italy.
He said: “The south of Italy needs infrastructure.
“We need to move forward.”
But a few days later M5S minister Barbara Lezzi responded: “We do need infrastructure: we need roads, schools, train stations.”
Italian environmentalists claim Puglia will suffer as a result of the pipeline.
They fear it will contaminate freshwater supplies, turn the beach into a building site and threaten the habitat of local Mediterranean monk seals.
But interest in the pipeline has been on the rise in Europe as opposition grows to plans for the larger Russian-backed alternative gas pipeline, Nord Stream 2.
Countries such as Poland, the US and the UK fiercely oppose Nord Stream 2.
They argue it will strengthen Russia’s influence in Europe, weaken Ukraine’s economy and entrench the power of Russian gas.