Derry City boss Ruaidhri Higgins reportedly turned down the chance to be considered for the Notts County job.
The Magpies are searching for a new head coach after Ian Burchnall left the club to take over at Forest Green Rovers. The board of directors have said the process could take "at least a couple of weeks" as they strive to find the right candidate.
A number of possible contenders have been mentioned, and Independent.ie reports that Higgins "was sounded out to see if he would be interested after being identified as a strong candidate". It is said that the 37-year-old would fit the bill based on the style and approach of his current team, who play in the League of Ireland Premier Division.
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However, the report adds that Higgins, who used to be Republic of Ireland chief scout and analyst, is happy at Derry and decided not to explore the opportunity at Notts any further. He only signed a new four-year contract earlier this year.
Luke Tisdale is favourite to succeed Burchnall, according to bookmakers BetVictor, having just left his role as head coach of Coventry City under-23s after seven years at the club.
Mike Williamson is next on the list, having just led Gateshead to the National League North title as player-manager. The former Newcastle United defender has also been linked with the Hartlepool United job.
Burchnall departed Meadow Lane shortly after the team's promotion bid was agonisingly ended by Grimsby Town in their National League play-off quarter-final tie.
Grimsby take on Solihull Moors at West Ham's London Stadium on Sunday to decide who join champions Stockport County in being promoted to League Two.
Meanwhile, Notts' manager hunt has not stopped other business being done. Wing-back Tobi Adebayo-Rowling has been signed, along with prolific striker Macaulay Langstaff from Gateshead, sparking talk of a possible swift reunion with Williamson.
Elsewhere, defender Richard Brindley has signed a new two-year contract with the Magpies, while Elisha Sam has left the club to pursue opportunities elsewhere.
A statement from the board of directors earlier this week (Tuesday) said they had been working hard to identify potential replacements for Burchnall, while also being "inundated with applicants".
They added: "This process has left us extremely confident of recruiting a head coach who will suit the club’s philosophy and seamlessly adjust to life at Meadow Lane.
"We would, however, like to manage supporters’ expectations over timescales as we expect it to be at least a couple of weeks before an appointment is made.
"We share the view of our fans that this is a very important decision for the club as we continue our pursuit of promotion to the EFL and, with the players not returning for pre-season training until late June, we see no benefit in rushing this process."