According to the Independent, Mr Varley is still locked in negotiations with other senior figures from the industry as part of the Project Merlin initiative and is likely to put proposals to politicians within the next few days.
"It is quite clear that the banks are not lending enough and in many cases are charging ridiculous rates," said Liberal Democrat Treasury spokesman Lord Oakeshott. "We hope banks will make us an acceptable offer."
Mr Varley is also understood to be discussing the issue of bonuses to see whether a compromise over business credit and bank bonuses, but it is unclear whether an agreed remuneration limit will be set.
The news came after Reuters reported that chief Treasury secretary Danny Alexander had told the BBC he expected financial firms to show "responsibility" over pay to assuage "justifiable public anger".
By Tony Aynsley