Bristol Port Company has applied to the government for approval for the scheme.
The company proposed that the terminal, which has been estimated to cost $1.2 billion, be completed by 2011.
The original cost of the terminal was estimated to be a third of that price at $390 million.
The company's proposal to the government was in response to a shortage of deep-sea container terminals in the UK.
This lack has been highlighted recently with the growth in containerised volumes, particularly from Asia, and resulting port congestion.
The government has already approved additional terminal capacity at several of the country's ports.