"I believe we can look forward to improved dialogue with the department," Brown said in a statement.
In a call with CNBC, Brown said he expects a deal can be worked out with Dinallo in 7 to 10 days.
Between 1999 and 2004, Brown ran MBIA and its main unit, MBIA Insurance. He joined the firm as a director in 1986 and retired last May.
MBIA, known in industry parlance as a "monoline" insurer, strayed from its core business of guaranteeing municipal bonds into the more lucrative but riskier activity of backing structured mortgage securities. That strategy fueled growth in the past decade but led to rising losses during the past year as housing sales sputtered and credit markets seized up.
Brown said in the interview that MBIA will be involved a major restructuring to divest itself of businesses involving collateralized debt obligations and other derivative transactions.
Shares of MBIA have plunged 83 percent in the past year, and the company has had to sell equity to bolster its finances even as it contends with high-profile investors betting against its shares.
New York regulators are trying to orchestrate a rescue so that bond insurers can maintain their triple-A ratings. There also has been talk of splitting up the companies to separate safe municipal bond activities from the woes associated with the mortgage business.
"In my view, the structure of the financial guarantee industry needs redesign," Brown said in an open letter to MBIA shareholders on Tuesday. He also said he would seek shareholder approval for his restricted stock award.
The bond insurer business model also must change, he wrote, to avoid the kind of capital-raising difficulties faced by MBIA and rivals such as Ambac Financial Group .
Prior to joining MBIA, Brown was CEO of Talegen Holdings, an insurance holding company, and CEO of Fireman's Fund Insurance.
He is currently serving as non-executive chairman of Safeco. He will step down from that position in May.
MBIA has raised more than $3 billion in recent months as it tries to maintain its crucial "AAA" financial strength rating. Ratings agencies have worried recently that bond insurance claims are likely to rise to unmanageable levels in the coming months due to rising defaults among mortgages.
Bond insurers essentially need a "AAA" rating to book new business.
The ratings agencies fear a recent surge in mortgage defaults will set off a wave of defaults among bonds backed by the troubled loans and insured by companies like MBIA. That potential jump in defaults would force MBIA to increase the number of claims it pays.
Moody's Investors Service, Fitch Ratings and Standard & Poor's have all downgraded other bond insurers, including Ambac and Security Capital Assurance . All have said they are reviewing MBIA's rating and recent capital-raising efforts to determine if the company has enough cash in reserve to cover future claims.
-The Associated Press and Reuters contributed to this report.