A previous plan to add a much larger addition was withdrawn under heavy criticism from preservationists.
The Texas Historical Commission will begin deciding between the plans later this month.
The mansion was severely damaged by a suspected arson fire in June 2008. No arrests have been made.
Renovations to the 153-year-old Greek Revival mansion had already begun when the fire nearly destroyed the building. Perry and his wife Anita had already moved to rented home in Austin -- at a rate of about $9,000 a month -- and have been there ever since.
Dealey Herndon, who manages the mansion project for the preservation board, said officials hope to be finished with the $26 million renovation in January 2012. That figure includes the total cost of renovation, including for work done on the house before the fire.
Historians are scrutinizing the project to make sure that as much of the mansion's original architecture, aesthetics and functionality are retained as possible. Herndon said objections over the first plan highlighted desires to not change the view of the property from the main entrance.
"We got a lot of push-back trying to improve the private quarters," Herndon said.
She said planners still wanted to update the private areas for future governors. She likes the larger of the two new plans because of its additional bedroom, which she said could be used as a home office, and the new bathroom.
That plan adds less than 1,500 square feet.
The Department of Public Safety, which is in charge of mansion security, has signed off on both plans, Herndon said.
Mandy Dealey, president of the Heritage Society of Austin said the group "applauds the change of direction in the proposals."
Although he presides over the Preservation Board, Perry declined to say which plan he liked better, saying he would leave it up to the historical commission.