If it was the club sending out a message to potential suitors about the player's availability, your point about bidding war would be totally on the money. However, that's not the case.
It's Rooney who wants out, and this weakens United's position significantly. If he isn't sold in January, he can buy out his contract in the summer for £5m and sign as a free agent for the club of his choosing with the sign in bonus that'll more than make up for it.
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All it takes is one club to be interested in buying him and everyone else will jump in. Thats what you do when a player of Rooneys reputation becomes available.
Its like how we rushed in when Newcastle went sniffing round. He'll be gone in January and there will be a large bidding war for his services. Ozil was in a similiar position and he went for a fair amount of money (albeit in the summer and not cup tied).