McAlpine has been working with the university for the past two years in preparation for the project.
But after recently winning tenders for two large new infrastructure projects it has now decided to focus resources on these.
A contract notice has now been issued by the University inviting expressions of interest in tendering for the £55m design and build contract.
University of Cumbria Chief Operating Officer, Mark Swindlehurst, said: “I’d like to thank SRM for all their work over the last two years getting us to this point and I know that they will be supporting us from the sidelines”.
He said: “We have a fantastic design ready to go and will now be going through a tender process to select a new contractor with a view to building work starting on site in early 2025.
“It’s an exciting time for the university, the wider city and region, as we move towards realising our vision and the next phase of delivery for this transformational project.”
The University of Cumbria and Cumberland Council are in the process of finalising new agreements for the transfer of the land and property owned by the council that is needed for the project.
Further surveys and ground investigations have also been completed, in order to finalise the designs, ahead of moving into the construction phase.
Funding for the £78m scheme is being provided by the Department for Levelling Up, Housing and Communities through the Borderlands Inclusive Growth Deal, and by the University of Cumbria, with additional funding for the Carlisle Business Exchange Centre coming from the Carlisle Town Deal Fund.
Firms have until June 24 to submit applications under a schedule that should see the winning bidder start work in January 2025.