The 30 year-old centre, set up to train disadvantaged people as garden retailers, is now open to offers from any retailer, with local rumours suggesting that it might become a pet shop.
Princes Trust chief financial officer Amy Stirling, who was appointed in February 2014, is believed to have scrapped the previous tender process, which had reached the shortlist stage, and started again with more than just garden centre owners being targeted.
A Prince's Trust representative said: "We are currently going through a process to identify a suitable buyer for the garden centre. We have received expressions of interest from various companies and will be assessing the potential buyers on a case-by-case basis.
"We have not yet set a deadline on finding a buyer. As a fundraising charity, our focus is supporting disadvantaged young people into jobs and we need to raise more than £65m a year in order to continue our vital work."
The trust bought two-thirds of the lease for Fulham Palace Garden Centre from the London Borough of Hammersmith & Fulham for more than £500,000 last year (HW, 30 March).
The charity took over from previous owner Fairbridge Trust in 2011 but said because its "main focus is supporting disadvantaged young people into jobs" it is "looking at all options for the future of the garden centre", which it sees as non-core in its operations.
The centre originally helped disadvantaged people to get back into work but has recently been used as a fundraiser for the trust, which helps disadvantaged young people. Manager Chris Webb is due to leave next month.