The France international is in demand after a series of sensational performances, and Pep Guardiola is said to have taken an interest.
Romania's Adrian Popa in action with France's Dimitri Payet
There is no denying the Frenchman is one of the most talked about footballers at the European Championships, after his superb performance and stunning goal in the competition's opener against Romania.
With the eyes of the world watching, Payet orchestrated proceedings, and proved that he deserves to be mentioned alongside the very best in Europe. Hammers fans are delighted in the attention their hero is getting, but the club will unsurprisingly also have to cope with a potentially more disruptive interest in the player, with football's richest clubs keen to test the resolve of Irons' owners David Gold and David Sullivan.
France's Dimitri Payet celebrates after scoring their second goal with team mates
With Paris Saint Germain already being linked by the Telegraph, Don Balon are now saying that Manchester City are interested in the 29-year-old, and with the ability to offer Champions League football and the opportunity to stay in the Premier League, the Citizens may well fancy their chances of catching Payet's eye.
However, quite aside from West Ham surely being hugely reluctant to even entertain the idea of selling their talisman, Payet would do well to look at who City already have at the Etihad, were he to deliberate the positives and negatives of such a move.
The former Marseille man has become a star after moving to East London, and must have cemented his place as a key member of the France side with his recent international appearances.
West Ham's Dimitri Payet celebrates scoring their second goal
Uprooting to a highly competitive club like City, who already boast huge attacking midfield threats such as Kevin de Bruyne, David Silva and the costly Raheem Sterling, could be perceived as a risk.
But the report states that Pep Guaridola is a huge fan of Payet, and rightly so after the last 10 months or so, and would be looking to play the Frenchman out left with De Bruyne sticking to a more central position. Both he and the City supporters may dream of the France international pulling the strings alongside Silva and De Bruyne with Sergio Aguero up front, and there is no denying that the Manchester outfit have financial clout that the Hammers would be unable to match.
Whatever substance there may or may not be in Manchester City's interest in the player, one thing is for sure, more performances like Friday and there are only going to be further rumours and heightened interest.
France v Romania - Euro 2016 - Group A