United Lincolnshire Hospitals Trust has lodged the plan for the unit to City of Lincoln Council.
It would include a single storey extension to help provide extra room and facilities.
Bosses at the trust said the plan is in “very early stages” but added that it would help to provide an extra MRI scanner, changing facilities and technical rooms.
Associate Director of Estates and Capital Planning at ULHT Chris Farrah said: “We are proposing an extension to the MRI suite at Lincoln County Hospital to accommodate additional diagnostic equipment.”
In its plans, the trust said the extra space will help to “address the increasing demand upon the service”.
Officals added that the project costs were not yet available as a business case would be put forward if the plan is given approval.
ULHT is facing increased demand at its hospital sites.
Further pressure on Boston Pilgrim Hospital’s A&E has led the trust to look for further funding for an expansion of the unit.
Health bosses are looking to create extra space at the department in order to cope and are in talks with NHS England over a possible capital bid.
Inspectors from the Care Quality Commission said the unit was suffering from “significant overcrowding”.