The 22-year-old has impressed for Middlesbrough in the Championship and is out of contract at the end of the season.
“He is a good, young player but we have respect for him and the club,” Mancini said. “We will see.”
“We haven’t made any bid for Adam Johnson,” Bruce said.
“It’s fair to say we have had discussions with Middlesbrough, but we haven’t put in any formal bid.”