The 27-year-old has been at St James' Park since a controversial switch from rivals Sunderland in 2014, making 102 appearances for the Magpies thus far.
According to the Daily Mail, Colback was already training away from the main group earlier this week when, after one player picked up a knock, he was called to join in.
Colback, however, is thought to have refused to take part, infuriating Benitez, who then reportedly told the player to train alone.
The report goes on to claim that Colback reported to the club's training ground on Friday afternoon, after the senior session had finished, and trained by himself.
Colback has two years remaining on his current Newcastle deal.