The National Wildflower centre closed in February when the charity Landlife, which ran the centre since its opening in 2001, went into liquidation.
Petition organiser Caz Black said: "We must protect this vital community resource from closing and for the international significance of the research of transforming urban green spaces with locally-produced wildflowers the centre provides to continue."
The centre is situated in Court Hey Park on the outskirts of Liverpool. The venture provided seeds and information on UK national wildflowers, eco-therapy to a range of groups, display gardens which were open to the public, made wildlflower meadows, held the national wildflower collection, and was a location for learning about biodiversity, health and wellbeing.
Hodder & Partners designed the £1.35m visitor centre building. The Big Lottery Fund put more than £2m into the project.
Former chief executive since 2012 Tony Jones says the centre needs £500,000 to re-open.
The Eden Project's Tim Smith has made an unsuccessful bid to take over the centre and said it still hoped to help save it. But wildflower stocks and equipment are being shipped out.
David Moore and Martin Maloney of Leonard Curtis of Liverpool were appointed liquidators in February.
Company accounts show income dropped to £351,000 in 2016 from £577,000 in 2015, with a loss of £136,000 in 2016.
The NWC said in December: "The National Wildflower Centre finances have been increasingly challenging during this time of continuing austerity and it is with great sadness that its trustees have decided to wind down all business operations by February 2017.
"During these challenging times trustees and staff are exploring with partners opportunities to secure a legacy for the National Wildflower Centre that sustains its valuable activities, assets and values."