The Spanish international Ramos has two years left on his deal with the La Liga giants.
Koscielny put pen to paper on a new contract with the Gunners last year. He signed for the club from Lorient in 2010, and has since turned into one of the best defenders in Europe.
Reports in Spain have claimed that the 29-year-old Koscielny is Real's No 1 target should Ramos leave to join United.
United have made a £30m bid for Sergio Ramos (Getty Images)
Koscielny has made 201 appearances for Arsenal, with the club winning two FA Cups with him in the side. He was named in the Premier League Team of the Season in 2013/14.
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