The government is also offering to convert its shares in Lloyds TSB/HBOS
Royal Bank of Scotland will convert the £5bn of preference shares it has sold to the Treasury into ordinary shares, BBC News has learned.
This will take the bank a step closer to full nationalisation, giving taxpayers a 70% stake - up from 58%.
The move would stop RBS having to pay the 12% fixed dividend that preference shares attract - worth £600m per year - and could allow it to increase lending.
The Treasury is proposing a similar move with the merged Lloyds TSB/HBOS.
BBC business editor Robert Peston said: "In theory, if the two banks didn't have to pay this dividend, they could lend £27bn more every year."
Ordinary shares - give you voting rights at general meetings, and pay a variable dividend depending on profits
Preference shares - give you no voting rights, but pay a fixed dividend irrespective of profits
The government invested in both types of shares in RBS, Lloyds TSB and HBOS as part of its £37bn bail-out last October.
But the banks have complained that the commitment to pay such a large dividend, regardless of their profit levels, was prohibitive.
The Treasury could help by converting its shares in the new Lloyds Banking Group - which begins trading on Monday after the merger - to take its stake past 50%.
This would remove an annual dividend commitment of £480. However, Lloyds is said to be unhappy about the government gaining majority control.