According to Sky Sports, former Arsenal midfielder Vieira will hold talks with Newcastle this week.
The former France international midfielder is on the staff at Manchester City as an elite development coach at the moment, but his current contract runs out this summer.
Owen, a former Newcastle striker, believes that appointing Vieira would be a risk, but it could eventually pay off.
'@donhutch4 Risky but could be a master stroke if it comes off. I think he feels it's time to make the next step. Done his apprenticeship.— michael owen (@themichaelowen) May 31, 2015
Vieira has experience of coaching at youth level, but it could be too soon for him to take charge of as big a club as Newcastle.