The Cavaliers are now on an 11-game winning streak with José Calderón starting at point guard.
Rose had been in contact with coach Tyronn Lue in recent days. "We will continue to provide him with support and have patience as he re-joins his teammates and works his way back on to the court".
Rose has played in only seven of the Cavs' 23 games this season due to an ankle injury, and frustration with his injury led him to a almost two-week self-imposed exile in which he contemplated retirement.
Rose's career has been slowed by knee injuries.
Wade has notched a pair of 20-point games during this winning streak after reaching that mark just once in his first 14 games.
Rose's comments were brief and delivered to the team on the court before the Cavs readied themselves to face the Sacramento Kings, the source said. "You know he's a quiet guy".
While Lue didn't disclose the content of Rose's message, he said the team was happy to have him back at the practice facility. Hopefully he wants to use us. He was fined by the Knicks and apologized to his teammates when he returned the next day.
Rose, 29, flew into Cleveland early Monday morning and plans to report to the Cavaliers' practice facility, ESPN.com reported.
Rose signed a one-year, $2.1 million veterans minimum deal to join the Cavaliers this season. However, the three-time All-Star took it upon himself to clear the air. The Chicago Bulls selected him with the No. 1 pick in the 2008 National Basketball Association draft.