Shropshire Council have applied for permission to build the structure, which will also contain a kitchen, seating area and toilets, next to the existing play area.
A design statement says the leaf-shaped timber building will have a “natural feel” and “blend in to the surrounding environment”.
Councillors will discuss the proposal when they meet on Tuesday, September 17.
Planning officers recommend they vote in favour of the centre.
In a report before Shropshire’s North Area Planning Committee, planning officer Tim Rogers said: “The proposed building would be of a unique design constructed of timber with roof/canopy and decking area taking the form of a leaf.
“The canopy and the roof overhangs will be supported on natural tree trunks.
“The proposed development will provide an improvement to an established and popular tourism and recreational facility at an important local attraction.
“The proposed building is considered to be well designed for its unique setting and would have a minimal impact upon the character and appearance of the natural landscape, the conservation area and nearby listed building.”
A design statement, prepared by Flights of Fancy Creative Play Ltd – which designs play equipment and other structures made from sustainable wood – says: “All timbers will be left to weather down naturally to further blend in to the surrounding environment.
“The natural feel of the building will be further enhanced with the addition of a ‘live’ gutter, creating a foliage border around the building.
“The building will be heated by a sustainable air-sourced heating system.”
Ellesmere Town Council discussed the application when it met on July 1, and voted to support it.
Minutes of that meeting state: “It was felt that the design and materials of the proposed building were sympathetic to the surroundings of Cremorne Gardens, and that the facility would be a valuable asset for the Town.”