The project will involve upgrading Outering Road from a single lane to a dual carriageway.
The Sh2 billion project has not been completed since May 2012.
Kura has advertised for a consultant to prepare a plan to ease traffic jams on city roads.
The project will cost an estimated Sh250 billion ($2.5 billion).
Local firms did not meet the financial threshold set by the government.
The facility, which will constitute 3,300 solar panels, will generate 1,256MWh a year.
The government is building 4,120km of roads countrywide.
Sections of the highway are damaged, with broken drainage covers.
Thika Road completion has also seen several shopping malls being rolled out along the route.
The road is inspired by the N1 highway that runs from Cape Town to Harare.