Djokovic invited Becker's partner Lilian and oldest son Noah into his centre court box for the second match running and saluted the pair after seeing off Kokkinakis 6-1 6-4 6-2 on Wednesday.
The three-time defending champion then delivered a heartfelt message to Becker's family and his mentor, who helped guide the Serb to six of his 20 grand slam titles during a three-year union together that ended in 2016.
A six-time grand slam champion and former world No.1 himself, who won three Wimbledon crowns, Becker is currently serving a two-and-a-half-year jail sentence. He was found guilty of hiding £2.5 million ($A4.4 million) worth of assets to avoid paying off debts after declaring bankruptcy.
"We've been through a lot together during those three years of collaboration," Djokovic said.
"Our relationship dates back even before that. Of course, after we finished our professional relationship, we always stayed close, him with my team, with my agents, with my family.
"Of course, it breaks my heart to see what's happening to him. I can only imagine how hard it is for his family members. So, of course, this is a little gesture of friendship to invite them.
"He knows and they know that they can always count on me for whatever support or help I can provide."
Djokovic said he hadn't been in touch directly since Becker was sentenced in April.
"But I've been communicating to him through them," he said.
"Noah and his younger brother Elias are going to visit Boris, I think, in the next few days for the first time since he went to prison.
"I've just been trying to give support to people around him, his closest people, his family members, because I consider Boris really a family member, someone that I greatly appreciate, respect, and care about."
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