The mid-tier investment bank has appointed Lloyds, Royal Bank of Scotland and UBS to manage the investor meetings, they said.
Close Brothers declined to comment on the speculation.
The group is made up of three businesses – banking, asset management and securities, which includes the Winterflood brokerage business, the biggest contributor to operating profit in the firm's last financial year.
Last year Close Brothers sold its corporate finance division to Daiwa SMBC Europe for a net £67m. It also spun off Close Growth Capital, a private equity unit, via a management buyout.
In September, the bank reported an 11 per cent fall in annual operating profit to £113.7m for the year to the end of July 2009. In January, the bank said it had done well in the first five months of its current year.
Since the beginning of the year the corporate bond market has been very active.