The 29-year-old point guard, who took part in the team’s training camp in San Diego last week, faces being unavailable for all Nets home games if he opts not to get vaccinated.
Golden State Warriors’ Andrew Wiggins said last week he would not get the shot, meaning he would miss all of their home games due to San Francisco’s similar vaccination protocols.
But Wiggins eventually got the shot, with expectation for Irving to take similar action.
“No further update,” Nets coach Steve Nash told reporters about Irving on Tuesday.
“We support him. We are here for him. Things change. When there’s a resolution, we’re here for him.”
Nash tried to play down the situation but the potential to be without Irving for 41 games would be significant for one of the NBA’s title favourites.
The Nets bowed out of the NBA Conference semi-finals to eventual champions Milwaukee Bucks last season.
“I’m not really worried about anything,” Nash said about practice.
“We’re just trying to work every day. We came in today and had a great practice and we’ll do the same tomorrow, and that’s kind of where I leave it.”