Its current facility in Church Lane does not meet the standards of the England and Wales Cricket Board, and members are planning a new clubhouse, football training pitches, parking area and access off Selby Road.
Meanwhile, a retirement "care village" of 64 apartments and 29 bungalows could be created at the old ground after demolition.
The club shares is facilities with the Garforth Rangers football club, which would also move to the new site.
A planning statement reads: "Garforth Cricket Club is currently located on Church Lane within Garforth and is a popular and important sporting facility serving the Garforth community. The site is in a prominent position in proximity to Garforth town centre.
"Having played cricket for over 85 years at Church Lane, Garforth Cricket Club’s facilities are significantly outdated and do not meet the required standards of the England and Wales Cricket Board.
"As a result, the Club has been looking for a new facility for some time and has recently managed to identify a potential new home nearby at Selby Road.
"The club owns the Church Lane site. However, the size of the club’s existing ground and facilities are inadequate for the current level of participation at this highly active and successful cricket club, and restricts its continued progression.
"Indeed, the existing club house is substantially below standard and smaller than what is typically required to accommodate the facilities associated with successfully running a cricket club.
"Garforth Cricket Club therefore wishes to relocate to a larger and more suitable site that is able to meet its current and future needs, and has been looking to do so for a number of years. Following a search for sites across the Garforth area, the cricket club identified the land at Selby Road in Garforth as the only site in this area which is both available and suitable to meet its needs."
Care home developers Morbaine Ltd have said that by providing much needed accommodation for older people, the plans will "optimise the use of this sustainably located site with an attractive new development" while also supporting local businesses.