The new Manchester United coach included the Roma star on his six-man summer shortlist, but the player's representative says any sale would be decided only by the Serie A side.
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The new United boss included the 24-year-old is his six-man shortlist of desired transfer targets, but is currently sidelined with a serious knee injury until the autumn.
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Strootman and Van Gaal have built up a relationship through the Netherlands national setup, but agent Chiel Dekker insists any sale would only be sanctioned should Roma see fit and not the player himself.
"He won’t be back playing until autumn - that’s the time schedule at the moment," Chiel Dekker told The Guardian. "He is of interest to Louis van Gaal but not related to Manchester United at this point."
When probed as to whether he would be of greater interest in the future, he added: "[He] could be. But he’s in Rome and he had a terrific season. There has been nothing between the clubs or between Louis and Kevin - they know each other and like each other but at this stage its not related to Man United.
"Roma do not want to sell. The first thing is its all between [the] clubs. And it's also a very difficult decision because he has to choose between a fantastic club in Rome, a club that bought him and supported him while he was injured and [then] you have his personal coach of the national team at United.
"The clubs have to decide. He’s very happy at Rome, he’s happy to stay because they will play in the Champions League next season, and he is happy to recover from his injury, so at this stage we are not part of any discussion."