The National Executive Committee and the National Council of the NDC are currently in a meeting to discuss the nomination.
The President is expected to join the meeting later in the day.
Many lobby groups within the party have argued against the re-nomination of Mr. Amissah-Arthur as running mate, citing his low public visibility.
But the Central Regional branch of the party has kicked against the move, explaining that the Mahama-Amissah-Arthur ticket is the only guarantee for victory in the 2016 general elections.
Some names that popped up as possible replacements for Mr Amissah-Arthur include Hannah-Tetteh, Foreign Minister and the Speaker of Parliament, Edward Doe Adjaho.