Klopp has been open about his admiration for the winger and Liverpool considered a move to sign him last summer.
While the Reds have Diogo Jota and now Luis Diaz on the books, they are continuing to plan for the future, with both Sadio Mane and Mohamed Salah set to turn 30 this year.
West Ham are keen to keep Bowen and are plotting to hold talks with him in the summer over a new deal.
He still has over three years left to run on his present contract at the London Stadium, but the Hammers want tor reward him for his progress and also secure his future for the long term.
They could be tested with offers for Bowen in the summer and are keen to strengthen their position.
West Ham splurged £20m to sign Bowen from Hull City in the 2020 January transfer window.
The wide-man has made 35 appearances for West Ham so far this season, scoring 12 goals and providing eleven assists as he plays a key role in the club’s push for a top four finish in the Premier League.
