Highly placed sources said the agency might close its ongoing inquiry as it would lead to multiplicity of investigations.
The sources said the Economic Offences Wing of the Mumbai Police has the professional expertise and is competent enough to investigate the case.
They, however, said the agency is open to probe the alleged irregularities in the working of the Exchange if government or any competent court directs it to do that.
Based on these complaints, the agency had started a preliminary enquiry to look into all aspects comprehensively.
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The Exchange has been facing problems in settling Rs 5,600 crore dues of 148 members and brokers, representing 13,000 investor-clients, after it suspended trade on July 31 on the government's direction.
Yesterday, the Economic Offenses Wing of Mumbai Police arrested Amit Mukherjee, vice-president at NSEL's business development department, for his alleged role in the scam.
BJP leader and Investors Grievances Forum president Kirit Somaiya had recently filed a PIL in the Bombay High Court stating that NSEL forged/manipulated documents regarding stocks and liquidity and allowed some of the companies to pledge the same stock with more than one financial institution.
There are 24 buyers/members who have to pay Rs 5,600 crore to the spot exchange for settling dues of the investors.