But the club won't rush their brilliant playmaker - and new minority stakeholder - into a decision on his playing future.
Savarese has been in touch with last season's Johnny Warren Medallist and former Spain, Manchester United and Chelsea midfielder, who wanted to take a break before deciding on his future.
"I have had conversations with him. Of course the club wants him to come back. It's the desire not only from the club, but from me as well, from the coaching staff," Savarese said on Tuesday.
"He's a class act in everything, not only as a player, as a human being.
"We want to make sure that this decision is made by him.
"He has the right to make the decision if he wants to have one more year with us.
"Of course, we are pushing in a little way to make that happen, hopefully, but I do think at the end it will work out the way he wants. And I think we need to respect that."
New A-League Men coach Savarese, who started last month as Arthur Diles's replacement, has a long-standing relationship with Mata's father, player agent and former footballer Juan Manuel Mata Rodriguez.
Former Venezuela international Savarese, 55, said Mata's signature was the "most important thing" this off-season and was optimistic he would join his teammates in "hopefully the next few weeks."
The club isn't putting any deadline on the 38-year-old, who only joined Victory last September and had a sensational season before becoming a minority owner in June.
"We're giving him time to make the decision because he deserves the time. That's how much we want him to be here," Savarese said.
"And we'll see how it's going to go. But it's his decision, and I will continue to stay in communication with him, hoping that things are going to work out well.
"He's a person that's not going to leave the club too long thinking about what is going to happen.
"I'm sure he'll come at the right time to say what he wants to do."
The club is looking at contingency plans in terms of signings if Mata, who notched 13 assists and five goals last season, doesn't return ahead of their October 18 season opener.
Victory already had Japanese striker Charles Nduka and Brazilian winger Santos and have signed Welsh central defender Tom Lockyer and German Philipp Ziereis.
"The quality of the foreign spots have been very, very good for us - those that were here before and those that have arrived," Savarese said.
"I'll continue to say Mata as the last - the cherry on the cake - for us to be able to have the right group of foreign players here."
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