City Transportation Director Blythe Bailey said the cost for a permanent fix to the Wilcox Tunnel has risen by over $10 million.
He said the higher estimate is based on some recent soil samples. The results of the testing will add significantly to the cost.
When the city applied last year for a federal TIGER grant, the price tag was put at $54 million.
Now the estimate is $64,676,000.
The city is pledging to contribute $25 million.
The work would include keeping the current tunnel for traffic in one direction and building a new tunnel for the other lanes of traffic.
Councilman Russell Gilbert said this application might have a chance if the area Congressman and Senators will get behind it.
Councilman Yusuf Hakeem said he was advised that there were 5,000 applications filed last year for TIGER grants, and the Wilcox Tunnel ranked 197.
Federal officials said last year there were 627 "eligible applications" requesting $10.1 billion or 20 times the available funding.
The city recently completed a $2 million upgrade of the existing tunnel at Missionary Ridge. It was closed for several months during the work.