The West Ham United star has been linked to Real Madrid.
The Frenchman was one of the signings of the year last season, quickly becoming a star man in the Hammers midfield.
His performances did not go unnoticed as he was named in the PFA Team of the Year and subsequently in the France squad for Euro 2016.
He has continued his fine form at the tournament, starring in their first two wins as France made it to the knockout stages of the competition.
His displays have sparked talk that a big money move could be on the cards, with Le10Sport claiming that La Liga giants Real Madrid, currently managed by Zinedine Zidane, are keen on his signature.
Redknapp cannot see that happening though, saying he sees no reasons why West Ham would sell their star player so soon.
“I don’t think they'd sell him. West Ham have a new stadium, 60,000 stadium, Olympic Stadium, sold 50-odd thousand season tickets,” he told Betsafe.
“David Sullivan, David Gold, they aren’t into selling that club, it's worth a fortune. They won't be short of money; I don’t see a reason why they would sell their star player.
It will certainly be interesting to see if a big money bid for Payet does arrive in this transfer window.
His performances are unlikely to have gone unnoticed by the big teams in Europe, as he has arguably been one of the stars of the tournament so far.
Indeed, West Ham will probably be secretly be hoping he does not stand out as well in the latter stages to avoid any bids for his services.