The Spireites boss, 39, was suspended by the club on Monday ‘pending an investigation into allegations of misconduct’.
Rowe’s first-team coach Danny Webb has taken charge for now.
In response to a request for a comment from the DT, Derbyshire Constabulary said in a statement: "We are aware that Chesterfield Football Club have taken action to suspend a member of the club for allegations surrounding misconduct.
"Due to a person being named in the media we are not able to confirm or deny at this time that a police investigation is taking place in relation to this matter."
The police are not able to add anything further at this time.
Since the announcement on Monday afternoon, Rowe’s social media accounts have since disappeared.
He was appointed Town manager in November 2020 and led them from the relegation zone to the play-offs.
This season Chesterfield have only lost two of 23 league matches and they enjoyed a memorable day out at Chelsea in the FA Cup third round.
In a statement yesterday, the Spireites said: “Chesterfield FC can confirm that James Rowe has been suspended pending an investigation into allegations of misconduct.
“Danny Webb will take charge of the team.
“As the matter is subject to an investigation, the club is unable to make further comment until that investigation is complete.”
Chesterfield are next in action away at Eastleigh on Saturday in a game live on BT Sport (5.20pm KO).