However, for now, there is yet to be any official contact between the clubs.
Strootman is recovering from a serious knee injury that has ruled him out of Van Gaal's Holland squad for the World Cup in Brazil, with the 24-year-old not expected to play again until the autumn.
Agent Chiel Dekker told the Guardian: "Roma do not want to sell. The first thing is it's 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 play Champions League next season and happy to recover [from] his injury, so at this stage we are not part of any discussion."
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