Rather puzzlingly, Keown admits Tottenham win more games when the Argentine plays but would still prefer to see him omitted from the side.
And 20-year-old Dier, who struggled considerably after a few weeks at Tottenham, would be his choice to replace Fazio.
"The stats for Spurs winning when they [Jan Vertonghen and Fazio] play are remarkable. I think Vertonghen is a good centre-half and was surprised when [Younes] Kaboul was given the captaincy over him," the former Premier League defender said during a 'Tackle Keown' session on the Daily Mail website.
"Fazio is a weak link but managers like to pick players who win games. Sometimes he is slow and ponderous and he lost the ball when Chelsea scored.
"They have Eric Dier in the group who started well at right-back but could be a centre-back. I’d like to see him given a chance in the middle to get his confidence back up and develop his game."