SBI had earlier proposed to raise Rs 5,000 crore for the purpose.
"A proposal will be submitted to Executive Committee of Central Board (ECCB)… for approval for issuance of long term bonds of Rs 20,000 crore for financing of infrastructure and affordable housing in domestic and overseas market instead of Rs 5,000 crore intimated earlier," SBI said in a filing to the stock exchanges.
The bank did not specify whether the borrowing would be in rupee denomination or dollar.
The executive committee of the central board is scheduled to have a meeting on January 17, it added.
Earlier this week, SBI announced plans to raise up to $2 billion (over Rs 12,600 crore) by issuing bonds in US dollar or other convertible currency over two fiscals to fund overseas expansion.
It said the fund-raising will take place through a public offer and/or private placement of senior unsecured notes in US dollar or any other convertible currency during 2017-18 and 2018-19.
Last month, the bank's board had approved raising Rs 8,000 crore through various sources, including masala bonds, to meet Basel III capital norms.
Masala bonds are rupee denominated specialised debt instruments that can be floated in overseas markets only to raise capital.
The bank said it has time till March 2018 to raise the funds.
Banks in India have to comply with the global capital norms under Basel III by March 2019. Internationally agreed time frame for the same is January 2019.