McConnell pushed the issue last fall as Congress considered, and eventually passed, three free trade agreements with Colombia, Panama and South Korea. He offered an amendment to renew the authority, which failed.
At the time, White House officials said they weren't prepared to move forward on the issue.
Fast-track authority expired in 2007.
Kirk didn't provide a timeline as to when the administration would make the request but he suggested it may be sometime this summer, around the time trade officials have said they could complete negotiations on the TPP.
Kirk said he would consult with lawmakers to ensure the bill's passage.