According to reports, the Conservative minister will still seek to raise approximately Â£2.5 billion ($4.02 billion) per annum from the bank levy, but will tweak the tax so that firms with large Asian customer bases are not hit as hard.
The measure - originally announced by Mr Osborne in his emergency Budget back in June - is expected to affect around 15 British and overseas companies with significant operations in the UK.
"Having finalised the detailed design, we are now considering whether the rates proposed at budget are appropriate to deliver the expected yield," the Treasury said in a statement. "Rates will be announced when final draft legislation is published."
Standard Chartered and HSBC have been particularly vocal in their opposition to the scheme, warning the government that it could spark a major exodus of leading financial groups from London to foreign bases.
In addition, the two banks are believed to have expressed concern that Lloyds and the Royal Bank of Scotland - two of the major beneficiaries of controversial government bailouts - would be least affected by the tax in its initial form.
Senior figures at HSBC and Standard Chartered implied that excessive monetary punishment could prompt them to reconsider their decision to run their main bases from London, depriving the British taxpayer of revenue in the long term.
The duty is poised to come into effect from January 1st 2011 and will affect the global liabilities of British-based groups and the UK liabilities of foreign companies with relevant interests.
Last week, British Bankers' Association and Barclays chairman Marcus Agius claimed in a letter to prime minister David Cameron that UK banks are being hit harder by regulation than those in some other countries.
By Asim Shah