Mats Hummels is flattered to be attracting interest from over Europe but has no intention of leaving Borussia Dortmund.
If Danny Rowe departs Rotherham again this season it will only be to Wycombe, according to Millers boss Steve Evans.
The club confirmed that assistant Mark Venus would take over from the 49-year-old, who has been at the helm since 2010, until a permanent successor is appointed.
A statement on their official website read: "Middlesbrough Football Club have today announced that manager Tony Mowbray has left the club with immediate effect.
"Assistant manager Mark Venus will take charge of the team until further notice."
Boro have won just two of their first 12 league games this season and currently sit 16th in the Championship. They went down 3-2 at struggling Barnsley on Saturday.
The statement continued: "The club would like to place on record their sincere thanks to Tony Mowbray for all of his substantial efforts, dedication and integrity.
"He leaves with the very best wishes of all at the club.''
Mowbray, the former West Brom and Celtic boss, has been unable to guide Boro out of the Championship in his three seasons in charge.
He finished 12th, seventh and then 16th last season, while things are panning out little better during the current campaign.
Boro's next game is at home to Doncaster on Friday night.