The 46-year-old tactician joined the club in October 2009 and led the club to victory in the Europa League last season, defeating Fulham 2-1 in the final.
However fortunes have not been so bright this season with the club surrendering their Europa League crown, exiting at the group stage, while they sit in eighth place domestically with hopes of European qualification for next season slipping from their grasp.
Relations between the coach and the club's hierarchy have soured of late with it being suggested that Flores would turn down the offer of a contact extension.
Yet this is unlikely with it being reported that Miguel Angel Gil and Enrique Cerezo had lost confidence in the former Benfica coach months ago.
Flores remains on good terms with the club's sporting director Jesus Garcia Pitarch who is also set for a summer departure as the club look towards a managerial and boardroom shake-up.
Several names are being linked with the Atleti job including Gregorio Manzano, Joaquin Caparros, Unai Emery and Luis Garcia, with all four coaches currently in employment.