Highly placed sources said that inquiry is in the final stages and statements of Bhave and former SEBI member K M Abraham have been recorded.
The sources said a decision on whether to convert it into a regular case for carrying out further probe or to close it will be taken by senior officials of the agency by end of this week.
According to CBI, the PE was registered on issues of alleged irregularities in granting sanction to the MCX Stock Exchange (MCX-SX) by the Securities and Exchange Board of India(SEBI) in 2008 and renewing its recognition in 2009 and 2010.
MCX-SX was set up by Shah-led Financial Technologies India
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Ltd (FTIL) and its commodity exchange arm MCX and began functioning as a full-fledged stock exchange last year after a prolonged battle with SEBI.
The exchange was initially granted permission for only a limited segment of currency derivatives in 2008, on the condition its license would require approval every year.
Bhave had slammed the CBI move, saying the agency was indulging in "pick and choose" while registering PE against him and Abraham.
Last year, SEBI asked MCX-SX to restructure its board and governance structure after a payment crisis broke out at the National Spot Exchange Ltd (NSEL), also promoted by FTIL.