The former Liverpool, Warrington Town and Bala Town midfielder joined last summer from FC United of Manchester and was a key member of the Purps side throughout the season until it was curtailed by the pandemic.
He made 14 appearances during the 2020/21 campaign, scoring five goals.
Manager Michael Ellison said: “I’m delighted Burkey has committed for another season. Along with his performances on the pitch, his mentality, professionalism and the standards he sets are second to none.
“He’s been a pleasure to work with in the short time we’ve been here and I’m looking forward to working with him in the season ahead.”
Burke added: "I have enjoyed my time so far with the Purps. I am looking forward to this season and having spoken to Ello I can see that the club means business.
“I can’t wait to get started.”
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