The Sunday Times reported that Hands is said to have talks with a number of advisers, including Goldman Sachs, about launching an auction.
Terra Firma hopes to get £700m for the chain of 153 centres, which has added about 30 centres since it bought Wyevale for £276m in 2012.
Turnover increased to £290m in results released in July 2015, up 5.1 per cent. Concession income and gross margin rose as did operating profit.
Terra Firma had hoped to build the chain up to 200 centres before selling but some sources suggest the number of garden centres willing to sell is dwindling.
Wyevale's delayed transactional website is yet to launch, so there is work to do at the chain, but the chain has hugley increased its concession numbers to more than 500, making the purchase more attractive to future investors.