The 26-year-old made the switch to Upton Park in January 2012 from Championship outfit Barnsley and helped the club achieve promotion to the Premier League via the play-offs.
He started Tuesday's 2-1 victory over Cheltenham Town in the League Cup and notched the opening goal.
But a lack of game time in the Premier League has seen Vaz Te grow frustrated, with manager Sam Allardyce apparently willing to allow the Portuguese to leave.
"In my 10 years as a professional football player I have never submitted a transfer request nor issued a statement," Vaz Te said in a statement to Sky Sports.
"However, I am frustrated at West Ham United Football Club.
"Last season I was asked to change positions for the benefit of the team even though I had just scored 24 goals.
"The main objective was to finish top 10 in the Premier League and I followed my instructions to the best of my ability as the club always comes first.
"As a result, even though I was injured for three months, no other player made more assists than me and no other winger scored more goals than me.
"In addition, since I joined this football club on January 31, 2012, no other player has scored more goals than me in all official competitions to date.
"Statistics are evident to all, despite this, it has been made obvious to myself and my representatives that I am not in the manager's plans.
"Therefore, it is with a heavy heart that I submit a transfer request and look to join a club where my approach to the game will be appreciated."
The club would not comment on the issue when contacted by Perform on Thursday.
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