Local residents are being asked for their views in a consultation exercise which runs until 11 August.
Under the proposed partnership with Middlesbrough Council, Askham Bryan would develop the facility which will see area used as offices and storage space remodelled for the delivery of training courses including horticulture, floristry and animal husbandry for up to 400 students aged between 16 and 19.
The college will also provide demonstration competition gardens within the courtyard. Public access to the park, which has one million visitors a year, would not be affected.
Askham Bryan is also expected to bid for further grant funding to complete its programme of restoration work at Stewart Park.