The project is being led by Inverclyde Council in partnership Inverclyde Leisure with support from sportscotland, the Lawn Tennis Association (LTA) and Tennis Scotland.
Councillor Jim Clocherty, Inverclyde Council's depute leader and convener of education and communities, said: "This is a significant step forward in the development of our indoor tennis centre.
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"We have the potential here to add another top-class facility to the fantastic array of indoor and outdoor sports facilities we already have in Inverclyde, subject to planning permission of course.
"The weather can be so unpredictable so this development would complement existing outdoor courts throughout the area to allow tennis to be played all year round no matter the conditions and encourage even more people to pick up a racket and enjoy the sport."
The proposed facility would have three LTA approved tennis courts, a small soft play area, an Express Fitness Studio gym and a self-service café.
The development would complement the existing grass football pitch, changing pavilion and mountain bike trail at Rankin Park, as well as the neighbouring bowling club.
An Inverclyde Leisure spokesman said: "This is an exciting project that would enable a pathway for children through to clubs along with offering a toddler's soft play area and Express gym circuit to improve the health and wellbeing of our local community."
