Lewes Road recreation ground in Newhaven was transferred back to Lewes District Council from Kuwaiti European Holdings Company on August 8.
The district council said a goodwill payment of £10,000 was received from the company on August 7.
It pledged to use the money to deliver improvements to the recreation ground.
Leader of Lewes District Council cllr James Page said: “I am happy to continue conversations with Newhaven Town Council about the longer term future of the recreation Ground.”
A community group Riverside Park Community Voice is calling on the district council to hand this land over to Newhaven Town Council.