The Sunday Telegraph reports Cable will pursue the former bankers by disqualifying them from sitting on company boards.
The paper said it understood that a detailed legal report commissioned by the business secretary food that there was “prosecutable evidence” which can be used to bring about the disqualifications.
The report is known to be have been passed to Cable in recent weeks.
Alongside Goodwin, former head of RBS’s investment bank Johnny Cameron and a few other directors could be targeted.
The Telegraph said disqualifications can be brought about through the courts – which is thought to be more likely during this case – or through civil action. People can also volunteer for a ban.
The report said an announcement from Cable is likely within the next few weeks.