The Associated Press, citing the team's website, reported the move as official on Saturday night but on Sunday the story on the team's website reporting that Dooley had been hired was updated to say that the position had not yet been filled.
Dooley was fired in November after posting a disappointing 15-21 record in his three-year tenure with the Vols. His three straight losing seasons were the longest such stretch of futility for the storied program.
Dooley would take over in Dallas for Jimmy Robinson, who was not seen with the rest of the Cowboys staff this week while it evaluated players at the Senior Bowl.
Robinson has been Dallas' assistant head coach/wide receivers since 2011, joining the team from Green Bay after the Packers won Super Bowl XLV.
Robinson has helped develop Dez Bryant, now the Cowboys' top receiver. A source told ESPNDallas.com's Todd Archer that Robinson could move into a consultant role with the team after a 23-year run as an assistant coach with six teams.
Dooley was Miami's tight ends coach when Dallas head coach Jason Garrett coached the Dolphins' quarterbacks under head coach Nick Saban in 2005-06.
The Cowboys' receiving corps, led by wide receivers Bryant and Miles Austin, and tight end Jason Witten, finished the season third in the NFL in yards (4,992) and yards per game (312.0) behind the New Orleans Saints and Detroit Lions.
ESPN NFL Insider Adam Schefter and ESPNDallas.com's Todd Archer contributed to this report.