"The two unions have threatened to go on strike on December 20. Negotiations are going on with the government," an All India Bank Employees Association (AIBEA) functionary said.
The unions claimed that about 5 lakh employees of various public sector banks would participate in the strike.
The employees unions are saying that the amendment to the banking laws will dilute the interest of public sector banks.
The Banking Laws (Amendment) Bill, 2011, was taken up in the Lok Sabha on Monday, but no discussion could take place in view of protest by the opposition.
Among other things, the Bill seeks to increase the cap on voting rights of private investors in public sector banks to 10 per cent, from one per cent.
Finance Minister P Chidambaram has ruled out the possibility of referring the Bill for the second time to the Standing Committee on Finance for further scrutiny as has been demanded by Opposition parties.
Earlier in August, employees of public sector banks had gone on two-day nationwide strike opposing banking sector reforms and outsourcing of non-core activities.