In November last year, Enam sold the investment banking, institutional and retail equities businesses to the private sector lender.
The proposal to induct Bhansali on the Axis Bank board as independent director was a part of the deal.
The banking regulator, however, expressed its discomfort with a quid pro quo agreement when Axis Bank applied for regulatory clearances for merging Enam's arms.
Following RBI's discomfort, Axis Bank has formally withdrawn the proposal.
Sources said though RBI at this point in time does not favour Bhansali's induction, he can became a board member of Axis Bank at a later date.
"The regulator raised the issue on the quid pro quo arrangement -- where Axis picks up Enam's arms and in lieu, among other things, Enam's promoter gets a seat on the bank's board.
"As a result, Axis has withdrawn the proposal," said a banking industry source.
Axis Bank did not respond to an email sent by Business Standard on the issue. Bhansali said: "I have no comments on the issue, as the clearance of the deal is awaited from the regulator."
Last year, Axis Bank entered into an agreement to buy Enam's investment banking and equities business in an all-stock deal valued at Rs 2,067 crore (Rs 20.67 billion).
The deal was expected to close within six months from the date it was signed.
It was proposed that Enam Securities would demerge its investment banking, institutional equities, retail equities and related businesses, such as distribution of financial products, to a wholly owned subsidiary of Axis Bank.
Manish Chokhani was named managing director and chief executive officer of the newly formed entity.