The Dutch ace has long been linked with a transfer to the Bernabeu.
Club president Ramon Calderon had the capture of Robben as one of his prime objectives when he was elected to the post last summer.
And now it appears that he will finally get his man.
Reports in Tuesday's English papers are claiming that Chelsea have upped their asking price for the talented former PSV star to a whopping £27million.
But the latest reports coming out of Spain suggest that a move to the capital is imminent for Robben.
His father Hans told Spanish daily AS that he was hoping the deal would be completed on Monday, but is still banking on it going through in the next 48 hours.
He said on Monday night: "We hope that the agreement between Real Madrid and the Chelsea can be closed tomorrow. Between now and Wednesday we think that everything can be solved."
Robben Sr added that negotiations are still at a delicate stage, saying: "My son cannot make any sort of declaration or grant any interview until the agreement between Madrid and Chelsea is reached."
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