National Museums Northern Ireland (NMNI) and the Belfast International Arts Festival want to host the art installation at the Ulster Museum.
Belfast City Council is submitting a separate bid to host the ceramic poppies at Belfast City Hall.
The full artwork, called 'Blood Swept Lands and Seas of Red' consisted of 888,246 poppies on display in London.
Created by artist Paul Cummins and designer Tom Piper, it marked 100 years since the start of World War One and drew more than 5m visitors.
After the attraction was dismantled in November 2014, most of the poppies were sold in aid of six armed service charities.
However, two segments - 'weeping window' and 'wave' - of about 6,000 poppies each, were preserved to be displayed elsewhere in the UK.
So far, they have only been on show in Yorkshire, Northumberland and Liverpool.
In 2016, they will be displayed at four locations in England, Scotland and Wales.
Bids to host the poppies in 2017 must be submitted to the organisers 14-18 NOW by Monday 29 February.
In a statement to the BBC, NMNI confirmed it was submitting a joint proposal with the festival to display the poppies.
Belfast City Council is also submitting a separate expression of interest to host one of the sculptures.
In a statement, it said it had advised the festival "that the council would be submitting its own bid and asking that organisation if it would wish to support the bid".
However, Belfast International Arts Festival is partnering with NMNI for a separate proposal instead.
There are two separate proposals to bring part of the Tower of London poppies sculpture to Belfast in 2017.