A £20million deal for Kroos was agreed when David Moyes was still in charge at Old Trafford and his successor, former Bayern coach Louis van Gaal, has said the move can go ahead.
Kroos, 24, flourished under Van Gaal at Bayern and is keen to work under his old coach again.
The same is true of Robben, who was one of Van Gaal’s first signings in Germany when he joined from Real Madrid for £20m in 2009.
The 30-year-old winger has recently signed a three-year deal but that is unlikely to discourage Holland coach Van Gaal, who will be working with Robben at the World Cup.
United are understood to have agreed a £27m fee with Southampton for left back Luke Shaw and Borussia Dortmund centre half Mats Hummels is a target.