The 22-year-old is regarded as one of the best young midfielders in Europe and has been strongly linked with a move to Manchester United.
United scout Martin Ferguson watched the midfielder in action at the end of last season, but the Red Devils did not make a bid.
“Strootman has had a good time in Eindhoven, but he decided that he wants to prove himself in a better league,” Strootman’s agent Chiel Dekker told the Dutch media.
“If an agreement is able to be reached with a potentially interested club, PSV will allow Kevin to leave in January.”
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Liverpool have unveiled their new home kit for next season, sticking with the hugely popular retro styling of the current shirt.
The reputation of the Premier League means it is the most popular and one of the most watched leagues in the world.