Manchester United manager Sir Alex Ferguson expects to see striker Ruud van Nistelrooy at training on Monday.
The 30-year-old Dutchman has been at the centre of summer transfer speculation and Ferguson has rejected an initial approach from Real Madrid.
"They have made an offer, we have rejected it," confirmed Ferguson.
"If they don't come back in and increase their offer, he won't be going and I would be content with that. It would not bother me one bit."
Real have warned they will "not be held to ransom" over Van Nistelrooy, who Ferguson values at £16m.
"He is a striker who can score upwards of 20 goals a season and there are not many of those going around," the Scot said.
The Spanish giants are falling short in their valuation, offering just £12m, and vice-president Juan Mendoza said: "We are not going to drive ourselves crazy trying to meet valuations which don't bear any relation to the market."
German side Bayern Munich are also in the hunt for Van Nistelrooy if his switch to Madrid falls through.
"In the end it will be the player who has the final vote"
Real have failed with one bid for Van Nistelrooy, who has asked to leave Old Trafford, but The Bernabeu outfit still remain favourites to capture him.
However, Mendoza added: "We're about to reach the point where we break off all negotiations even though the player clearly wants to play for us.
"It's time to make it clear to Manchester United that Real Madrid are not going to be held to ransom over exorbitant prices."
New Real boss Fabio Capello said: "There is no question that I want Van Nistelrooy.
"The fact that Bayern also want him indicates that the entire market is being scoured by Europe's top clubs looking to snap up the best players.
"In the end it will be the player himself who has the final vote."
Meanwhile, Bayern Munich chairman Karl-Heinz Rummenigge admitted that the German side have not given up hope of hijacking Real's bid for Van Nistelrooy.
"We are trying to get him signed," said Rummenigge.
"The chances of him joining are changing by the day but we have not written him off."
Rummenigge is still confident Van Nistelrooy would choose a move to Germany over Spain.
"Every club wants to bring in important players, but it's the players themselves who have the final word," he added.
"There is a great relationship between the two clubs, and I know Van Nistelrooy wants to come to Bayern."
The Dutchman has scored 150 goals in 218 appearances since joining United from PSV for £19m in 2001.