Politicians say Daniels will be remembered for several initiatives including changes to the welfare system, I-69 and privatizing parts of state government.
The trustees are scheduled to talk about specifics of the contract on Friday, the first day of the two-day board meeting.
Tuesday's Statehood Day was held to celebrate Indiana' 196th birthday.
The governor says he wants his contract as Purdue University's next president to be an example of increased accountability in higher education.
Lugar says there are some in Washington who, for partisan reasons, find it acceptable to send the country over the fiscal cliff.
The governor told Chamber of Commerce officials they should improve on the policies from the past eight years, particularly with infrastructure and education.
All of the governor-elect's cabinet appointees were involved in Governor Mitch Daniels' administration.
The governor-elect chose Chris Atkins, who served under Governor Mitch Daniels, to lead the Office of Management and Budget.
Governor Mitch Daniels will speak at Indiana University's commencement in December before becoming president of Purdue University.
Governor Mitch Daniels led a crowd of people along I-69 on Monday to celebrate the opening of the interstate.