What follows is a list of five potential alternatives to the most frequently mentioned candidates:
1. Neven Subotic
More the rugged destroyer to the elegant ball-player of his defensive partner, the much praised Hummels, the Serbian may be a better mach for United than the German. Currently feeling his way back from injury, his own indifferent form has coincided with some on-field turmoil for Jurgen Kopp's side. A more pragmatic character than Hummels, happy to defend first and pass simply, allowing others to indulge in more creative moves, he could be far more what the flakey back four of Manchester United require. Both he and Dortmund may be more receptive to a move than Hummels in January, and he has the advantage of being both hugely experienced and, at 25, young enough to play at the heart of Van Gaal's defence for years to come.
At just 21, the VfB Stuttgart centre-half is one of Germany's newest internationals, and one of the country's most touted prospects. An intimidating 6ft 3", he never the less boasts touch and technique to distribute the ball comfortably, short and long, as well as offering the odd powerful stride into the opposition half. A relatively inexperienced candidate, and one, much like a young Rio Ferdinand, with the occasional tendency to place a little too much faith in his own ability to play his way out of tight spots. However, were United to wait a season or to for these flaws to be ironed out, they may find themselves having to pay two or three times the £10m Rudiger is estimated to be worth presently.
A player whose performances have been of such a calibre Celtic fans are wary of singing his praises for fear of drawing attention to him. A leggy, yet powerful and elegant defender, his qualities have seen him linked frequently of late with Arsenal, for whom a player of his type would seem an all-to sensible acquisition. With such all-round attributes, and for a relatively modest price, the 23 year-old would seem an ideal fit. However, there remain reservations. Not only could the step up from the SPL to the Premier League be a difficult one, but Van Gaal was not sufficiently impressed with the player to take him to the world cup in Brazil. Having been overlooked, it is difficult to know how highly Van Gaal thinks of the player, or even whether Van Dijk would want to play for him following his omission.
With a new contract still unsigned, Manchester United- and Arsenal- have both been linked with one of the Premier League's most consistent performers over the last 12 months, Winston Reid. An unspectacular choice, perhaps, but the New Zealand captain is renowned for his speed of thought, strength in the air, and lack of any discernible weaknesses in his defensive game. An ever-present in one of the league's meanest back-fours, the only doubt about his potential worth may be whether he can adapt to Van Gaal's philosophy of possession football, after developing his game under the notoriously prosaic Alardyce. But for Premier League experience at a reasonable price, there can be few better contenders.
One of Brazil's most outstanding defenders over the last four years, yet one cruelly overlooked for the international honours he deserves by choosing to remain in the Brazilian league. Renowned for his athleticism and the precision of his tackling, Dede has always been hesitant to move overseas due to concerns over living in a different culture, though he has not been short of offers. But, at 26, the time may be right for this mountain of the defender to fly the nest and make a case for himself as a starter in the Brazilian national team. The chance to work under Van Gaal, and to slot into a defence along side compatriot Rafael, could be enough of a draw for one of South America's untapped talents.