Disney bought the rights to the franchise from Paramount in 2013. Paramount Pictures distributed the most recent film in the series in 2008, the largely terrible Indiana Jones and the Kingdom of the Crystal Skull.
Rumors have surrounded Disney since the purchase, with both Bradley Cooper and Chris Hemsworth previously touted for the lead of the Indiana Jones revival. The company has yet to confirm or deny anything. Polygon has reached out for details and will update you when more information is made available.