Saban also said that Allen was the last of those targeted players who was left on the board when it came time for the Dolphins' pick.
The first preference was a front seven player on defense, with Saban mentioning the preference is "always big people."
There were six defensive linemen or linebackers among the first 15 picks, and the belief is that Florida State defensive end Kamerion Wimbley clearly was among those players the Dolphins had targeted -- Saban flew to Tallahassee during the week to work him out.
Saban said the Dolphins had discussions with the St. Louis Rams, originally picking 11th before they traded down three spots with Denver, and Cleveland, which had the 12th selection before moving down one spot in a trade with Baltimore.
The decision was made not to pull the trigger on one of those deals because the Dolphins came into the draft with only six picks, and only three before the seventh round.
"When you're giving up a 3, that's a price to pay," Saban said.
The Dolphins also had the opportunity to move down to acquire more picks, but they decided against it because they liked Allen and didn't want to bypass the chance to take him.
"We didn't really try to trade down," Saban said. "We had the opportunity to trade down but decided to pick the player we had targeted."
So what was it about Allen that so appealed to the Dolphins?
Start with the obvious, which is the size/speed ratio of Allen, who is a shade under 6-1 and runs a 4.4 40-yard dash. There's also his versatility, which he evidenced by starring at both free safety and cornerback at Tennessee.
Saban was asked by the NFL Network specifically about USC offensive tackle Winston Justice, who was available after some had once considered him a potential top 10 pick.
"We didn't consider Justice," Saban said. "We had several defensive players rated higher than Justice."