"Dean is highly regarded within the game and could have taken the opportunity to move. He received an overwhelming offer that would have been beneficial to him both on a personal and professional basis," said Machala.
"I am delighted Dean has chosen to remain as manager of Aldershot Town Football Club and I have to place on record my sincere appreciation to an individual who has proved his loyalty and integrity.
"We have a close bond throughout the club and are all genuinely excited as we enter the 20th year of Aldershot Town FC.
"We hope that the strength of our ambitious manager's decision will continue to show that there is a solid and settled infrastructure at the club and that the confidence in how the organisation is operated will bring more supporters to come along and watch league football at the EBB Stadium for the new season.
"We continue to be committed in doing our best for the benefit of our supporters."
Crawley director of football Steve Coppell is understood to have spoken to Holdsworth - who signed a one-year extension to his Aldershot contract last month - about taking over from Sean O'Driscoll at the end of last week.
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