The 26-year-old Manchester United academy product joined Ipswich on a free transfer in the summer and has started two of the last four league games for the Blues.
On Wednesday, Kieran McKenna decided to start Tuanzebe in the back instead of Woolfenden, who has started 16 games for Ipswich so far, against Millwall.
Mills admitted that Tuanzebe looks like a top player and believes that the former Red Devils star is a carbon copy of Woolfenden.
He pointed out that Tunazebe has a bit more experience than Woolfenden, but believes that the 26-year-old has not done enough to replace the Ipswich academy product at the heart of McKenna’s defence.
“He does look like a class act”, Mills said on BBC Radio Suffolk.
“He looks really to me a sort of almost a carbon copy of the man he replaced, Luke Woolfenden.
“They play with a lot of comfort; they are casual players; they read the game really well; they are good on the ball, their selection of pass is invariably the right one.
“The only thing that Tunazebe’s got is a little bit more experience than Luke Woolfenden has, but I would not diminish what Luke has done and Luke has done terrific for us this season as he did last season.
“He is a good player, Luke and I would not really like to say Tuanzebe on what he has done tonight, deserves to take his position.”
Tuanzebe has made three appearances for Ipswich in the league so far and now all eyes will be on McKenna to see whether he will get another opportunity in the Coventry City game at the weekend.