Pucovski was substituted out of Victoria's Sheffield Shield game on Saturday after a volleyball hit him on the head during the warm-up.
It was the 11th concussion of the 24-year-old's frequently interrupted but hugely promising career.
Pucovski is now resting at home in Melbourne and waiting on further medical advice, while prominent commentators have questioned his future in the game.
But Graf said the one-time Test opener is eager to continue his career — at least for now.
"He's realistic, he understands that this is bad and if it keeps going it can't be good for his health long-term," Graf told SEN on Monday.
"He does understand that, but being a young lad he still wants to play.
"It is so frustrating for him because he knows where he could be if he was fit and be able to get through multiple games.
"He's realistic about it, but he's still very much in the corner that he wants to keep playing and we'll support that.
"However, if the medical advice is contrary to that, we need to have a very hard discussion."
Victoria coach Chris Rogers and CV boss Nick Cummins have both labelled calls for Pucovski to retire to protect his long-term health premature.
The latest "fairly innocuous" incident has created plenty of concern.
"It was a ball that just scraped his face and he was OK, then he started to get a little bit of a headache," Graf said.
"He went back out and he fielded but he had to come straight back off, he felt nauseous and they're all the symptoms of a concussion.
"Very disappointing, disappointing for him but also disappointing for the team, it threw us into a bit of chaos for about half an hour."
Pucovski scored 54 in Victoria's first innings against South Australia, playing his first match since suffering a concussion during a training session in October.
"Prior to this, he (Pucovski) had discussions with the medical staff and they were starting to get worried, obviously so many concussions even though they are minor now," Graf said.
"We're talking with his management, he's got to talk to his manager, his dad, and work out where he wants to be and then have a chat with us.
"But from a sports point of view, obviously we're really worried."
