It is understood Kroos has already spoken to German team-mate and United star Bastian Schweinsteiger about life at Old Trafford.
United are also keeping close tabs on Chelsea target Miralem Pjanic.
The Bosnia & Herzegovina midfield sensation has a £37m buyout clause in his Roma contract, with United ready to hijack the Blues’ bid to take him to Stamford Bridge.
Meanwhile, boss Louis van Gaal has backed new teenage sensation Marcus Rashford for an England call-up.
Rashford, 18, is the talk of football after coming from nowhere to score four goals in his first three appearances.