The Hammers enjoyed an impressive first season under Slaven Bilic.
The Hammers enjoyed an impressed season last year under Slaven Bilic as they challenged for a top four place for much of the year and eventually secured a Europa League spot.
Key to their impressive performances was Payet, who was their star man following a summer move from Marseille.
He continued to shine for France at Euro 2016 earlier this summer and now Redknapp has backed him to go on and lead the Hammers into the top four in the years to come.
“There is no reason they can’t be a top four, top five team in years to come,” he told the club’s official website.
“Dimitri Payet is the leader of the pack now and he’s a fantastic talent, but they’ve got lots of good players. The club is in great shape, so let’s hope they have another fantastic season.”
It now remains to be seen whether West Ham can build on their fine first season under Bilic next time around.
Their hopes will of course rest on Payet, who they will be hoping does not get hit by the second season syndrome that has affected a number of players down the years.
The rest of their transfer business will also be key and if they can secure the striker that they want, there is no denying their hopes will be given a major boost.