Jack Russell (97), who took part in the Second World War operation, hopes to be among 300 servicemen on the Voyage of Remembrance from June 2nd to 9th.
Each veteran can take one guest. But Jack cannot leave his wife behind or take her on board without help from family as she has severe dementia.
His daughter, Helen Folds, said: "We're really proud of Dad. It'll be a shame if he can't go because he's always wanted to return to Normandy and he knows it could be his last chance to do it.
"But if he leaves my mum at home, she'll be screaming. There'll be chaos. When she's with him, she's calm.
"My dad looks after her 24/7 so he deserves a holiday.
"And it would be extra special because it's their 75th wedding anniversary this year. Mum wanted to get married in the apple blossoms of May but they had to bring it forward to February because Dad was training for D-Day."
Arena Travel, which is organising the trip, will provide an on-board team of carers and medical experts to help look after vulnerable passengers.
But Jack's daughter, Hazel Guy, added: "My mum wouldn't let someone else look after her. I can't even have carers in my house because she doesn't like strangers handling her. She'd be in hysterics. She'd scream the place down."
The sisters hope their cousin Lynn will join their parents on the trip to help take care of June while Jack takes part in on-board activities.
"Lynn visits my parents every other weekend to help out," Hazel said.
"Mum's calm if Lynn handles her because she knows her. And if there are only two beds in each room, Lynn could sleep at the side.
"Dad is quite fit and healthy so he doesn't need a lot of care.
"Mum can't walk but Dad can dress her and push her around in a wheelchair."
But Cheryl Duke, an employee of Arena Travel, said the company might not have space for Lynn because it has received more applications than places.
The company has also arranged two alternative trips: a coach to Normandy; or a three-night tour of the National Memorial Arboretum, Staffordshire. Both options allow each veteran to take up to two guests.
Helen Warrington, product manager of Arena Travel, said: "The coach journey is ideal for anyone who would struggle on their own. At that age, not everyone is fit and healthy.
"To be pretty blunt, the ship is not a care home but we do need to make sure the passengers will be OK. We wouldn't let anyone struggle. We just want to make sure everyone will be safe and that we can get passengers into lifeboats if there's an emergency."
But for Jack, the cruise to Normandy is a once-in-a-lifetime opportunity.
Hazel said: "Some of his mates were on the air force, and a lot of them didn't come back. He seems to have blanked out a lot of his war experience so it will be good for him to share stories about D-Day with people who've been through it, who know what it's like. It'll probably bring back memories.
"It's on his wish list is to go on the boat trip. My dad's in his late 90s now so there's not many chances left to go."