The Hammers are in the hunt for a new boss having parted with Sam Allardyce at the end of this season, bringing an end to months of speculation that the veteran boss would not be extending his stay at the club.
Likewise, Klopp is leaving Borussia Dortmund in the summer after a highly successful period at the club, during which they have won the Bundesliga, the DFB-Pokal and reached the Champions League final.
His final game in charge was Saturday’s German Cup final against Wolfsburg, with the coach remaining adamant he has not agreed a deal with another club.
While a move for the German remains unlikely, there is potential that owners David Sullivan and David Gold could sell the club to him with their forthcoming move to the Olympic Stadium after next season a big selling point.
If not, the paper claims that the Hammers remain keen on former Everton and Manchester United boss David Moyes, despite him insisting he will stay at Real Sociedad, while there is also a list of other potential candidates being drawn up.
They have, however, not set themselves a deadline for an appointment, although they would prefer to have a new man in charge within the next few weeks as the club shapes their squad ahead of next season.