Arsenal have already had a bid rejected by Liverpool for Suarez.
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The race to sign Luis Suarez looks set to hot up as Real Madrid will shortly submit their first official bid to Liverpool for the Uruguay international, the Daily Mirror reports.
Madrid have been linked with a move for Suarez all summer and Los Blancos is believed to be the strikers preferred destination following several comments by the Uruguayan in the media.
Reports in Spain suggest that Madrid will finally make a formal approach for Suarez and are set to offer Liverpool £10 million plus Gonzalo Higuain.
Liverpool have no real interest in signing Higuain and will reject the bid quickly, telling Madrid that they will only consider bids of £40 million and they will also insist that Suarez hands in a formal transfer request.
Madrid had been hoping to wait until nearer the end of the transfer window before making a move for Suarez but they have had to make an early bid because of the interest from Arsenal.
The Gunners already submitted a £30 million bid to Liverpool which was rejected but they are set to come back with an improved £35 million offer.
Suarez has stated that he wants to leave Anfield this summer to play in the Champions League and he has recently said that he is flattered by interest from Arsenal.