The report claims Madrid will sanction a loan move for Spurs target Morata if they secure a replacement - with Robert Lewandowski and Luis Suarez the club's top two targets.
Spurs are desperate to strengthen their attacking options in the January transfer window, with £26m man Roberto Soldado the club's main goal threat this term.
Jermain Defoe and Emmanuel Adebayor have both been linked with January exits, but Spurs want to bring in reinforcements before they move on squad players.
Morata was a target for Tottenham over the summer, but Madrid boss Carlo Ancelotti refused to entertain the notion of letting the young forward leave - even as part of the Gareth Bale deal.
But the La Liga giants may agree to let him leave if they can sign a replacement, with Lewandowski and Anfield hero Suarez top of the shopping list.
Liverpool forward Suarez was reportedly keen to talk to Madrid over the summer, and publicly agitated for a move after the Anfield hierarchy refused him permission.
But he stayed with the Reds, and is currently the Premier League's second highest scorer with nine Liverpool goals.