Despite rejecting United's recent £52m bid for the Spaniard, according to Lopez, Real have had a new deal presented to them.
When asked by Calciomercato if Morata had already agreed to a deal, Lopez said: "I can say there's a very important proposal and the decision rests with Real. I cannot tell [if it will be done quickly], we'll see."
Los Blancos are reportedly holding out for £78m for the 24-year old, but United view a fee under £70m as appropriate.
There has also been talk of interest from AC Milan in Morata, but Lopez has labelled their bid as insufficient.
Morata managed to bag 20 goals in all competitions for Real last season, but he failed to solidify himself in Zinedine Zidane's starting XI.