Taylor's agent, Gary Wichard, even has been quoted as saying his client wasn't thrilled with the idea.
But Saban made it a point to address the issue on Wednesday.
"We have no intention of moving or trading Jason Taylor," Saban said in the statement. "Everything we have done is to build our defense around what Jason does best. He's an outstanding player and we want him to be a focal point of our defense. We will use him in schemes that best feature his talents."
The latest signing was that of linebacker Donnie Spragan, who comes over after starting 14 games for Denver last season.
Spragan should compete for a starting job, probably the strongside linebacker spot vacated by the departure of Morlon Greenwood via free agency.
Spragan, who can play both inside or outside linebacker, had 67 tackles with a sack in 2004. He originally entered the league as an undrafted free agent out of Stanford in 1999 and has been with the Broncos since joining their practice squad in 2001.
Before Spragan, the Dolphins also signed defensive ends Kevin Carter and Vonnie Holliday, as well as safety Travares Tillman.
Carter and Holliday are both 6-5, 290 and perfect fits for the 3-4, but either also could line up at defensive tackle in a 4-3.