Councillor Graham Swift, deputy leader and cabinet member for resources, enterprise and economic development at Harrogate Borough Council said talks were still being held with the owners of the parkland - the Duchy of Lancaster - but it was "probably not possible" that a deal could be struck before all lockdown restrictions are due to end on 21 June.
The idea has been put forward to assist hospitality businesses with social distancing by giving them room for outdoor seating, although councillor Swift said it would only benefit "one or two" bars.
Speaking at a meeting yesterday, he said: "Some of our licence companies are very keen to see usage of the Stray under controlled licensing conditions and the reality is this will be challenging.
"The Duchy of Lancaster are rightly positive defenders of the space and for us to jump through some of the hoops required around the legal side to allow one or two companies to extend their footprint will probably not be possible before 21 June when the government fully opens lockdown."
The parkland is protected by an act of Parliament, the Stray Act 1985, which has restrictions on how it can be used including an annual limit on events.
There is also a requirement for the public to be consulted on some changes and Harrogate Borough Council said it planned to launch a survey on the idea to give businesses space if talks with the Duchy progress. Councillor Swift added:
"I have some sympathy with the licence companies that would like to flex their space but the reality is there is going to be a considerable opening up of spaces over the next few weeks.
"I hope that people will be able to take off trade and picnic on the Stray and utilise the space as we get more and more conformable with social engagement."
Under the government's roadmap out of lockdown, hospitality businesses will be allowed to reopen for outdoor service only on 12 April when customers can meet in a group of up to six people from different households or any number from two households.
Then, on 17 May, they will be able to seat customers indoors with the same household rules, while groups seated outside must be smaller than 30 people.
The final date in the roadmap is 21 June when all restrictions are due to be lifted.
By Jacob Webster, Local Democracy Reporter