Nick Blackwell is said to be in a stable condition in hospital after undergoing surgery to reduce swelling on his brain.
Blackwell, who does not have a licence to fight, was hospitalised again on Saturday following a sparring session, but BBC Sport reports that the Welshman is thought to be on the mend.
Upon hearing the news, Eubank Jr tweeted: "Nick Blackwell is back in hospital, after he tried to start sparring again. He's a tough, tough kid, I know he'll get himself through it again.
"I honestly hope everything is OK and the procedure he's had is not a serious one."
The British Boxing Board of Control will begin an investigation on Monday to find out why Blackwell was back in the ring.