Talks between the US investment bank and Automated Trading Desk are reportedly at an "advanced stage", according to the Wall Street Journal.
Should the talks progress as planned it is thought that an announcement of the finalisation of the deal might be delivered as early as this week.
It is thought that Citigroup is looking to acquire the firm so as to increase its market share in trading US stocks, while bringing under its roof computer programmes that will boost its drive to trade stocks in overseas markets.
Automated Trading Desk was founded by Rutgers University finance professor David Whitcomb in conjunction with two computer programmers in 1988.
Last year the firm handled around six per cent of the trading volume in major US stock markets.