While speaking in the National Assembly, Prime Minister Abbasi said that a serious allegation has been leveled against the former prime minister.
"In the current [political] conditions, this falls within the ambit of pre-poll rigging", he remarked.
He noted that general elections will be held in Pakistan in two months and the NAB is making allegations that the former premier was sending money to India.
NAB is likely to summon an SBP official to get their point of view on the issue. He also favoured setting up a special committee to probe the matter. The political future of Sharif, who leads the country's most powerful political family and his party, has been hanging in the balance since then.
The truth should be brought out before the people, he said.
Nawaz Sharif is already facing NAB references in an accountability court, which accuse him of concealing facts and being employed in an offshore company, owned by Sharifs son.
According to another report in the same newspaper, the Supreme Court has ordered the accountability court hearing the corruption references against the Sharif family to conclude its proceedings by June 9.
He also mentioned the graft-cases now being heard by the accountability court in Islamabad, saying they (PML-N) was not expecting justice.
Highlighting NAB's "bias" against Sharif, the premier quoted the saying, "Justice should not only be done but seen to be done".
Dastgir demanded a probe against NAB's internal workings and processes of determining investigations.
The Supreme Court of Pakistan had disqualified Sharif a year ago, forcing him to resign from the country's top post. He has also been disqualified from holding public office for life. Sharif has dismissed the corruption charges as politically motivated.
It clarified that the decision to launch the probe was taken on the basis of media reports and that it is well within its jurisdiction to probe money-laundering related matters.
NAB ordered on Tuesday an inquiry against Nawaz and others for allegedly laundering $4.9 billion to India.
According to NAB, World Bank's migration and remittance book released in September 2016 carried information that foreign exchange reserves of India increased by $4.9 billion after receiving the huge amount sent through money laundering, inflicting losses to Pakistan's national kitty. Moreover, the State Bank of Pakistan (SBP) said the estimates showed in the WB report were based on "assumptions" which did not reflect the reality.