The Clarets are guaranteed to finish seventh in the Premier League this term, meaning that they will be present in next season's Europa League.
Garlick is hopeful that the club will be able to keep Dyche 'for another five years', but has conceded that the 46-year-old's success will make that difficult.
"There will always be interest in him as long as we continue to punch above our weight. That is normal. We get used to that, it is just a fact of life," Garlick told reporters.
"It is the price of success, but as long as we continue to progress and be competitive we're always hopeful that he will be with us five years' time."
Burnley will finish their Premier League season at home to Bournemouth this weekend.