Several groups have made preliminary offers to buy all or part of the U.S. subsidiary of Israel Discount Bank, the lender said on Wednesday.

In a statement to the Tel Aviv Stock Exchange, Discount Bank said it had received an unnamed number of preliminary offers for Discount Bankcorp, the U.S. subsidiary that controls Israel Discount Bank of New York. The bank said it also received several preliminary offers to buy all or part of its Discount Bank Latin America unit. Two days ago, Discount's board of directors gave permission to buyers to begin due diligence.

Shares of Discount, Israel’s third-largest bank, rose 2.2% in Tel Aviv Stock Exchange trading to NIS 6.01 on Thursday.

Discount aims to sell either a 30% or 100% stake in the New York bank, whose shareholder equity at the end of June stood at $813 million. In the first half of 2013, the bank posted an $18 million profit, reflecting a 4.4% return on equity. Sources say that Discount Bank will not sell the New York unit for less than $900 million.

The sale of Discount Bank New York is being managed by the investment banks J.P. Morgan Chase & Co. and Sandler O'Neill & Partners. Several weeks ago they opened an information room for prospective buyers, which representatives from an estimated 20 different groups have since used.

Along with Mercantile Discount Bank, a domestic subsidiary, Discount New York is one of Israeli bank's most profitable assets. Should a sale go through, it will substantially help Discount boost its core capital adequacy ratio to the 9% required under Basel III guidelines by 2015 as required by the Bank of Israel.

Following an increase in profitability and a reduction in its holdings of high-risk assets, Discount's Tier 1 ratio of capital to risk assets reached 9.1% in June, under the less strict Basel II guidelines. However, under Basel III, its core Tier 1 ratio comes to just 8.6%.