Wild guided Halifax into the National League play-offs for the second time in three seasons this campaign, but The Shaymen lost to Chesterfield 2-1 on Tuesday night.
After the game, when asked about his future, Wild told the Courier: "It's not for now, I need to go home and reflect, sit down with the players and take it from there."
According to the Northern Echo, League Two Hartlepool, who were previously rumoured to want Wild as their manager, are again considering him for the role and have declared an interest in him.
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But Wild continues to be heavily linked with a move to Barrow, who released a statement ten days ago saying an approach had been made to an unnamed manager's current club to ask permission to speak to him regarding their vacancy and agree appropriate compensation.
Wild is under contract at Halifax until the end of next season.