Midfielder Flitcroft, 33, who signed an 18-month deal with the Blades after leaving Blackburn on a free transfer, said in the Yorkshire Post: "I could have joined Leeds United, but I felt that Sheffield United had more ammunition to get up this season. It was close and I had long talks with Leeds because Sam Ellis is a good friend who put me on the road to my career when I was at Manchester City.
"I felt indebted to listen to what Leeds had to say. They could have come up with anything, but I still wanted to go with the lads at Sheffield United."
Blades boss Neil Warnock thinks Flitcroft's leadership qualities and ability to "hold things together" in midfield will be a major asset to his side over the remaining 18 games of the season.
Kevin Blackwell wished Flitcroft good luck with his choice, but stressed he was happy with his existing midfield options. "In an ideal world, it would have been great to have him in the club, but I am happy with the players I have got. I am not disappointed in anything at all because we will only do things at our pace and that are right for Leeds."