On 23 November 2012 Konate signed a first team contract on a youth basis with Malmö FF. Konate made his Allsvenskan debut for Malmö FF in an away fixture against AIK at Friends Arena on 17 April 2013. He was substituted on in the 85th minute. Konate played a total of six matches during his debut season for the club, most of these matches was as an oncoming substitute, coming on for Ricardinho. After returning to the club halfway through the 2014 season Konate made 11 appearances as he competed for a spot in the starting line-up against regular Ricardinho. Konate's breakthrough came when he was selected to start in the deciding qualifying game against Red Bull Salzburg on 27 August 2014 in which Malmö FF qualified for the group stage of the 2014–15 UEFA Champions League.
Konate went on loan to newly relegated Superettan side Östers IF for the duration of the 2014 season with an option to return to Malmö FF in the summer of 2014. At the same time he renewed his contract with Malmö FF for an additional four years. Konate made 15 league appearances for Öster before being recalled to Malmö FF in the summer of 2014 to cover up for Miiko Albornoz and Mahmut Özen, two defenders that had left the club during the summer transfer window.