The couple want to make alterations to an existing outbuilding, which is a protected structure, put in place a new staircase, shower room and timber decking.
The planning application, which is with Wicklow County Council, also includes plans for a partial re-pointing with lime-based mortar and other repair and renovation works.
Day-Lewis (55) moved to the county 15 years ago and was given the Freedom of Wicklow earlier this year.
The two-time Oscar winner said that he enjoys living there because he can go "quietly about my business".
"I have been completely absorbed into the nobility of the Wicklow hills around me," he said. "This is the place that sustains me. This is where I have planted myself. It is a refuge where I restore myself."
The My Left Foot actor lives with Rebecca, who is a writer and director, and their two sons, Ronan and Cashel.
Day-Lewis has starred in films including My Left Foot for which he won his first best actor Oscar, There Will Be Blood, winning his second best actor Oscar, Gangs Of New York and In The Name Of The Father.
He plays Guido Contini in the new musical Nine alongside Penelope Cruz, Kate Hudson and Nicole Kidman. It is due to be released on December 26.
In an interview, the actor said that travelling to the west of Ireland when he was younger provided him with some training for his new role in the musical.
"In the Ireland of the past, when I was younger, if you went to somebody's house and had a drink, sure enough there would come a time when you would be asked to get up, it would be your turn," he said.
But the actor said that he has no further plans for the big screen in the near future and will return to relax in his Irish home.
"I'm very happily retired for the moment," he said. "I always think of these periods after work as in integral part of the work in a way, as they go hand in hand with the work itself."