The former Liverpool and Tottenham Hotspur midfielder is a Marmite figure among football fans.
But despite his Spurs background Redknapp does have some affinity with Hammers fans given his dad Harry spent much of his career with his boyhood club as a player and manager.
'I love watching him play'
Redknapp told Sky Sports: "He (Payet) makes me want to go and buy a West Ham season ticket."
"He is all class and a joy to watch – the touch, the way he goes past players and his passing is fantastic.
"He's an incredible player.
"I love watching him.
"The guy is absolutely magnificent and as I say, a total joy to watch whenever he's on the ball."
'Join the queue'
The praise was well received by the West Ham fans who feel it is about time their side started getting some credit after a brilliant season so far under new boss Slaven Bilic.
But Jack Sullivan, son of West Ham co-owner David, has delivered a cheeky response to Redknapp's comments on Twitter.
"(Jamie) Redknapp, well you can join the priority list now! For next season."
Payet is a bona fide Hammers hero
Redknapp went on to eulogise more about the former Marseille playmaker saying he had even outshone City's Spanish superstar David Silva.
Payet is fast becoming West Ham's biggest hero since Carlos Tevez and Paolo Di Canio.
While his skills and attacking prowess have been dazzling the Upton Park faithful, it is his workrate and tracking back which has impressed them just as much.
He is surely the signing of the Premier League season and is certainly playing his part in making the Hammers' last ever season at the Boleyn a memorable one before they depart for the 54,000 seater Olympic Stadium in the summer.
With players like Payet they will have no trouble filling the extra seats.