Jon Rahm won the Irish Open in Portstewart in 2017 and again in Lahinch this year
Castlerock Golf Club offers to organize the Irish Open in 2021, with initial discussions with European Tour officials who have already taken place.
Castlerock hopes to follow other locations in Northern Ireland as Royal Portrush, Royal County Down and Portstewart to host the Rolex Series tournament.
Tourism Northern Ireland is expected to support Castlerock's bid.
"We are aiming as high as we can and see where it takes us," said CEO Castlerock Bert McKay.
"It is the national championship and one of the biggest events on the European Tour now.
" We have seen the impact made on Portrush, Portstewart and Ballyliffin and it would be a rejection not to put the entire north coast on the map again between the Open Championships. "
Castlerock Golf Club offers to organize the Irish Open in 2021
It is understood that Northern Ireland is intended to organize the event in 2021 and 2023 with European Tour officials who want to visit the course at the end of the month to assess the club's prospects for organize the event for the first time.
McKay indicated that the first chats with European Tour Championship Director Simon Alliss and representatives of Tourism NI have been positive.
"Tourism NI would like to see the tournament coming back on the north coast, whether it be here or somewhere else," said the general manager of Castlerock.
"The discussions with the European Tour are at an early stage, but we will meet Simon Alliss and some guys from the European Tour in the next three or four weeks.
" We have the made some changes in the last 18 months, but we had to look at new tees and other bits and pieces.
"Lahinch is also a small village so if there is a will there is a way it would be the pinnacle of Castlerock and it would keep the focus on the north coast."