The 21-year-old was suspended for eight weeks by the ATP on Monday following his second round exit at the Shanghai Masters where he clashed with fans, the chair umpire and walked off the court midway through a point against Mischa Zverev.
The ban can be reduced to three weeks if he sees a sports psychologist, which Kyrgios had committed to, according to Australia's tennis association.
"I wouldn’t be surprised (if he quit) but hopefully that’s not the case," Cash told local radio station 3AW.
"Anybody’s got the opportunity to walk away but if it’s not good for his health then I think he should do that.
"But with some good things in place for his health and wellbeing, and a revised schedule ... he can go out there and enjoy his tennis, which is what we want to see."
Kyrgios posted a lengthy apology online after his Shanghai meltdown, which came only days after he won the Japan Open, the third and biggest title of his career.
The 51-year-old Cash, a notable hothead during the early part of his career, said Kyrgios was "flat and exhausted" when he arrived in Shanghai and should never have played the tournament.
He questioned the advice the Canberra native was receiving on tour and claimed Tennis Australia (TA) had failed to provide young players with the mental support to deal with the grind of the professional circuit.
"Mental health and understanding of where you are as a junior should be as mandatory as hitting forehands and doing stretching before and after a practice session," he said.
"I’ve talked to Tennis Australia about it and nothing has been done."
TA dismissed Cash's criticism as "incorrect," saying sports psychologists were available for players in every state.
"Sometimes they have access to two or three of them," TA spokesman Todd Woodbridge, the 22-times doubles grand slam champion, told Reuters.
"Tennis Australia's support is as strong, if not stronger than for any other (sport's) in the country,"
Cash said Kyrgios was "the next guy" in line for grand slam glory once proven winners like Andy Murray and Novak Djokovic bowed out.
"And who is standing up there? Well, Nick’s the obvious one.
"You tend to see after a great year, a bit of a lull, and (then) he’s got a great opportunity to grab a couple of grand slam titles and really be a success."
(Editing by Amlan Chakraborty)
