Glenvale Nurseries, owned and run by Helen and Duncan Varley, opened in 1993.
Berkshire-based developer Charlesgate Homes has now put in an application to build four houses on the site after removing the centre.
In its application, the developer says: "The current owners of Glenvale Nurseries purchased the garden centre 12 years ago but has seen a sharp decline in trade over the last five to six years which has had a huge impact in turnover to the point the current owners are finding it continually difficult to viably run it as a business.
"Mr and Mrs Varley have ploughed continuous amounts of their own money in to try and support the garden centre but due to the location and market trends it has come to a point where the garden centre will need to close."
It adds: "The current owners have run the current business since 2004 and you will see from the attached accounts that it is quite simply not viable to run this as a garden centre any longer and the only reason it has traded as long as is due to the current owners using their own personal savings to support the business.
"Other commercial businesses have been considered for this brownfield site but due to its close proximity to housing on all boundaries this would limit what sorts of commercial business can be run from here.
"To redevelop a brownfield site appears to be the most logical solution, bearing in mind the close proximity to existing houses."
Meanwhile, plots of land across Plymouth including a field near the Plymouth FC football ground at Home Park have been earmarked for developments, with a garden centre mooted for opposite Home Park, as part of Plymouth City Council's Joint Local Plan, which outlines long-term and potential projects planned for the city up until 2034.