Parkinson has a strong relationship with the club's ownership - which is buying him some time at the Racecourse Ground - after securing three promotions since 2021, as part of an incredible run.
However, after narrowly missing out on Premier League promotion last season, his start to 2026/27 has been poor with just two wins gained from 10 matches.
Former Burnley and Fulham boss Scott Parker has been linked as a possible replacement alongside ex-England and Liverpool captain Steven Gerrard.
Gerrard has not managed a side since leaving Saudi Pro League side Al-Ettifaq in January 2025 and he's open to a managerial return - as per TALKsport.
Wrexham's five matches up to the November international break will decide Parkinson's future as Gerrard awaits an update.