United want Morata because their top target Romelu Lukaku is joining Chelsea.
But Woodward thinks Bernabeu chiefs could try and strong-arm him i transfer talks.
He thinks the fact United refused to sell David De Gea could go against him.
So he will make one last bid of £60m to try and lure the Spain striker to Old Trafford.
Publicly Morata’s insisted he’s happy at Real Madrid – although he has hinted he may be open to moving if it means he gets more game-time.
Morata said earlier this week: “I want to be playing and to be important to the squad, particularly next year when there is the World Cup.
“But I want to fight for my place here, I would be crazy to leave Real Madrid. I would like to stay.”
His agent Juanma Lopez has offered United genuine hope a deal can be struck after admitting Morata has become frustrated at Real.
The striker’s agent, meanwhile, has give United hope a deal could be done.
Juanma Lopez said: “He does not want a season like this again. It was a great season, but he wants to play more.
“The player will take a clear and definitive decision in the coming days. I have not yet met with the representatives from Real Madrid.
“Alvaro is a player who wants to play a more important role. He wants to play more. Which is normal for an attacker who has scored 19 goals. It is too little.”
