PSV was the club where Zenden began his career, before moving on to Barcelona, Chelsea, Middlesbrough and now Liverpool.
PSV coach Ronald Koeman said: “Zenden is a good player with a lot of experience and we want to increase the amount of Dutch players.
“He has a warm feeling for PSV. We are really looking for these type of guys.”
Zenden has played down reports linking him with a return to Holland.
He told the Liverpool Echo: “I had a fantastic time at PSV, but I am not sure I have finished my job abroad to return to the Netherlands.”