Twickenham top brass have authorised the recruitment of a team manager and another specialist coach with Rob Andrew, the Rugby Football Union's elite rugby director, looking to fill both posts before the end of April.
Johnson, who led England to the 2003 World Cup, is favourite to become manager but Dallaglio has reservations about the former national team captain's credentials.
He told BBC Radio Five Live: "He was a fantastic player, one of the world's best players and one of the best the game has ever seen.
"But has he got enough hands-on experience working with a team in a different role to being a player?
"I'm sure he could slip seamlessly into that role provided he surrounds himself with the people that possess the strengths that possibly he hasn't got at the moment."