Crawley hope to have a new manager in place before their next home game.
Owners The SA Group have targeted finding Francis Vines' replacement by the time Reds play Southport at the Broadfield Stadium on November 12.
Vines was sacked on Monday following Crawley's embarrassing FA Cup exit against Ryman League Braintree.
General manager Paul Hobbs said: "That is the date we have at the back of our minds but the most important thing is to find the right person.
"We don't want to rush into it. We will advertise nationally and wait and see who is interested before we make any decisions."
Hobbs has confirmed there has already been interest in the vacant position and applications have included former international players.
He said: "The calibre of applicants have been very high. A few international players have been interested.
"I would imagine it is a good job to go for, so we are hoping to have more interest in the next couple of weeks."
Reserve team boss Murray Jones will take charge of the first team for Saturday's Conference trip to Cambridge United.
Jones, a former Brentford striker, joined Reds as a coach last season after a spell in charge of the youth academy at Crystal Palace.
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