Mr Abbasi, the former minister for petroleum and natural resources, is the principal accused in a National Accountability Bureau (NAB) case registered in 2015 over the award of a liquefied natural gas (LNG) import contract, Dawn News reported.
Other suspects in the case include former petroleum secretary Abid Saeed, Inter State Gas Systems (ISGS) managing director Mobin Saulut, private firm Engro's chief executive officer Emranul Haq and the Sui Southern Gas Company's (SSGC) ex-MD Zuhair Ahmed Siddiqui, the report said.
Mr Abbasi is expected to be elected as the new prime minister by Pakistan's Parliament tomorrow, replacing ousted premier Nawaz Sharif.
The Supreme Court on Friday disqualified 67-year-old Nawaz Sharif for dishonesty and ruled that corruption cases be filed against him and his children over the Panama Papers scandal, forcing the embattled leader out of office.
After Nawaz Sharif's disqualification, the PML-N nominated Mr Abbasi as its candidate for the prime minister's post for an interim period before Punjab Chief Minister and Nawaz Sharif's brother Shehbaz Sharif replaces him for the remaining 10 months of the government's term.
According to NAB documents, the contract for the LNG import and distribution was awarded to the Elengy Terminal, a subsidiary of Engro, in 2013 in violation of the Public Procurement Regulatory Authority (PPRA) rules and relevant laws.
The bureau registered the case on July 29, 2015, but it is still in the inquiry stage, contrary to NAB Chairman Qamar Zaman Chaudhry's claim that he has introduced a new strategy under which the process of complaint verification, inquiry, investigation and filing of reference takes 10 months, the report said.
It appears that like several cases of the Nawaz Sharif family, this one has also been dumped by the NAB, it said.
The case was registered on the complaint of Shahid Sattar, an energy expert and former member of the Planning Commission and the SSGC board of directors, along with others, accusing Mr Abbasi of misusing his authority and causing a potential USD 2 billion loss to the national exchequer in 15 years.
The NAB documents said that it had been recommended that the names of all accused in the case, including that of Mr Abbasi, should be placed on the Exit Control List (ECL) and the process was ongoing, the report said.
Talking to reporters after meeting Jamiat Ulema-i-Islam chief Maulana Fazlur Rehman yesterday, Mr Abbasi had said he was not afraid of any reference.
He said that those levelling allegations against him should search their own souls and be ashamed of their deeds.
"Not only one case but get registered 10 references against me," he said in reply to a question about Awami Muslim League chief Sheikh Rashid Ahmed's decision to approach the Supreme Court against him regarding the NAB proceedings.