The official said an announcement would not come before Thursday.
The person spoke to The Associated Press on Tuesday on the condition of anonymity because the person is not authorized to release the information.
Whipple, 53, was let go by Miami after Shannon was fired at the end of the season. He also coached Massachusetts to the 1998 Division I-AA championship.
UConn spokesman Mike Enright would not confirm the negotiations.
"We do not comment on the searches at UConn or any other school until the process is complete," he said.
Whipple's resume also includes head coaching jobs at New Haven and Brown. He served as an assistant coach with the Philadelphia Eagles before being hired by Randy Shannon in 2009. From 2004-06, he was the quarterbacks coach of the Pittsburgh Steelers, where he helped develop Ben Roethlisberger.
Since becoming a full Division I-A team in 2002, Connecticut is 65-46.