Wrexham chief executive Don Bircham says the club will not be rushed into appointing a new manager.
Gary Mills was sacked on Thursday after 18 months in charge of the National League club.
Bircham says the Wrexham board will consider a number of options before appointing a successor.
"It will be interesting when we get around the table next week to see how everybody's thinking," Bircham told BBC Radio Wales Sport.
"I guess we've gone down two routes in the past.
"We had Kevin [Wilkin] who was punching above his weight at a small club and we appointed him.
"We then went to the opposite end of the spectrum by appointing a very experienced man [Mills] who achieved success in our league."
Mills, who guided York City to promotion to the Football League in 2012, left Gateshead to succeed former Nuneaton boss Kevin Wilkin in April 2015.
Wrexham missed out on the play-offs in Mills' first season in charge and are currently 15th having lost four of their last six games.
Bircham said performances had not been good enough and after consideration the board were unanimous in deciding to part company with Mills.
"Results and performances were below our expectations," Bircham said.
"We've been watching it carefully and thinking hard about that and hoping there may have been a turnaround.
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"There was the odd glimpse of that which gave us some optimism, but all-in-all it's a results business and Gary accepts that.
"He was entirely dignified in our discussions. I had a very good relationship, as did all the board, with Gary and we're sad to see him go."
Bircham added that Mills' assistant, former Spurs and Reading striker Darren Caskey, remained under contract with the club.
Reserve team manager Joey Jones, head of youth Andy Davies and former club captain Dean Keates will be in charge for Saturday's FA Cup fourth qualifying round tie at Stamford.
"The club's in good hands for this weekend and there will be no major change for the players," Bircham added.