Chester's Deva Stadium home, which straddles the England-Wales border, has already been earmarked as a potential Welsh Premier League venue by The New Saints.
TNS have now opted not to persist with that application, club secretary Ian Williams admitting: "We made a formal request to ensure the use of the Deva Stadium facility for both domestic and UEFA fixtures, but we eventually ran out of time."
Should they be accepted, City would have no pathway back to the Football League and would no longer be allowed to compete in the FA Cup.
But Chester, whose fans are more in favour of becoming a 'phoenix' club and reforming within English football's pyramid structure, remain hopeful that they could become 'Welsh'.
"I am well aware of all the idiosyncrasies surrounding Chester's ground location," added Welsh Premier League secretary Deakin. "But the subject of whether to accept Chester into our league will be run past the board.
"I would prefer not to comment in detail about the application which was signed by Chester's club secretary.
"But, if Chester are accepted into the Welsh Premier League next season, it would have an effect on the league's plans to reduce the number of clubs in the division from 18 to 12."
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