TMW says Rashford's camp, along with United, are discussing four offers on the table. All proposals are for an initial loan, with some including an option to buy.
Along with Milan, Barcelona, Juventus and Borussia Dortmund are also in contact with Rashford's camp.
However, inside Casa Milan there remains a great confidence that the market will close with Rashford in the Rossonero colours.
Milan director Zlatan Ibrahimovic said over the weekend: "I know Rashford very well, I played with him when he was young. Now he is a man, he is confirmed as a great footballer.
"He is a Manchester player, I don't know if it takes much to convince him, everyone wants to play for Milan. It is a difficult operation, we haven't spoken to him yet. Let's see if we speak to each other.”