Rowett, who currently manages Derby County, said that he was approached by an agent who offered Lindelof's services to the Blues, but the 43-year-old rejected the Swedish defender.
The Rams boss told Sky Sports News: "About two or three years ago when we first went into Birmingham an agent called us and said we are trying to get some of our younger players out to expose them to different levels.
"We had a look at [Lindelof] and put it to some of the staff, but it was ironic because they felt he wasn't probably quite tough enough.
"Then suddenly he's been touted around at £20m or £30m. So I think we made a mistake. To be fair he got straight back in the Benfica side very quickly and of course went from strength to strength."
Lindelof failed to make the bench in three of United's opening four Premier League games, though he was involved in the Champions League win over Basel.