The Commonwealth Games Federation (CGF) confirmed the respective associations had lodged initial submissions for consideration.
"The Commonwealth Youth Games are an important, inspiring and impactful festival of sport, development and global friendship for the Commonwealth's most-promising young athletes," said David Grevemberg, CGF chief executive.
"We have received two initial bid submissions to host the 2021 Commonwealth Youth Games from the Commonwealth Games Association of Gibraltar and the Trinidad and Tobago Commonwealth Games Association.
"The CGF will now review these host proposals in detail in collaboration with the candidate cities, the CGF Executive Board and Management Team in order to be in a position to make an award in 2019."
The submissions will be discussed by the CGF at the organisation's Executive Board meeting in Singapore next month.
The CGF have been seeking a replacement host for the 2021 event since stripping Belfast of the right to stage the Games.
Belfast lost the rights to host the Games in June because of a lack of funding.
This followed political deadlock in Northern Ireland which means the required funding was not released.
A power-sharing coalition between the pro-British Protestant Democratic Unionist Party and Irish Catholic Nationalists collapsed in January last year.
Funds of £3 million ($5.4 million/€3.4 million) were not released by Northern Ireland's Government to the Northern Ireland Commonwealth Games Council (NICGC) and Belfast 2021 as a result of the political stalemate.
Trinidad and Tobago had announced in June they would consider throwing their hat into the ring to replace Northern Ireland's capital city as hosts.
Trinidad and Tobago Commonwealth Games Association President Brian Lewis confirmed their bid earlier today.
He tweeted the Opening Ceremony would be held in Queen’s Park Savannah on Emancipation Day, which falls on August 1.
Beach volleyball, aquatics and cycling are also set to feature should they be awarded the Games.
Esports and BMX Freestyle could also feature, according to Lewis, who claimed the Games would be funded in a joint public and private model.
Site visits are expected to take place to both candidates before 2018 draws to a close.