The £65m design and build job will also involve the redesign and potential redevelopment of its current site at Clatterbridge Health Park in Bebington, Wirral.
A satellite centre will remain in Wirral for outpatient chemotherapy and radiotherapy and Clatterbridge will run the new £100m Liverpool cancer centre.
Andrew Cannell, chief executive of the Clatterbridge Cancer Centre, said: “Building a new cancer centre on the same site as both The Royal Liverpool Hospital and The University of Liverpool offers the region a completely unique opportunity.
“It is our plan to take our outstanding care to a new level, bringing truly integrated cancer care along with life saving research, closer to even more patients across Merseyside and Cheshire.”
If proposals are approved it is hoped the new cancer centre would be ready to receive its first patients at the same time or soon after the opening of the new Royal Hospital in 2017.
Firms have until the 12 June to complete PQQs. More information is available from the e-tendering site.