The firms hoping to ride off with the job are: Bam Construct, Bowmer & Kirkland, Galliford Try, Interserve and Morgan Sindall.
They have submitted bids and will be told in three weeks, which has won the chase for the 5,000 seater arena with velodrome cycle track.
The project has been designed by Mace and will be built next to Derby County’s Pride Park stadium.
Mace Project Director, David Grose, said: “We have designed an iconic building which will complement Pride Park Stadium, but will also function as a stand-alone facility.”