The Croatian has been appointed as Tomic's interim mentor, following the indefinite ATP Tour ban handed to the 21-year-old's controversial father, John Tomic.
John was charged with assaulting his son's former hitting partner, Thomas Drouet, earlier this year.
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Zovko arrived in Australia last week and has already made a positive impression on Bernard, who is the second-youngest player inside the top 100 of the world rankings.
"He is starting to get into a good bond with my dad and team," the 51st-ranked Tomic told Australia's Channel Seven.
"It is still important to have my dad there; he is the one that brought me up and we spent a lot of time together.
"It is very difficult for me to let him go. He knows what is best for me and my tennis. Obviously this new coach is going to take his role and help out with my dad."
Tomic has targeted a spot inside the world's top 20 in 2014, having acknowledged that breaking the top-10 barrier would be tough.
"It is difficult to get into that group now, so maybe top 20 is a reasonable goal," he added.