Nevertheless, it remains to be seen if the England international - who is set to represent the Three Lions at Euro 2016 - will stay at Leicester or whether he will secure a transfer.
“Up front I suppose another centre-forward would be great, so you’d love to buy Vardy, but Leicester fans won’t thank me for that," he told West Ham's official site about the Leicester man.
"And he has [the Champions League] beckoning, so let’s develop one ourselves. I’m sure we must have kids in the youth system.”
West Ham, under manager Slaven Bilic, are definitely a team on the rise, but it seems unlikely that Vardy would join them - and who's to say they want them?
If rumours are to be believed, Bilic is after younger strikers this summer, amid speculation linking Hammers with the likes of Alexandre Lacazette and Michy Batshuayi.
They might need to replace Diafra Sakho in East London, with the Senegalese striker reportedly the subject of an £11 million bid from Sunderland (Sky Sports).
They have Andy Carroll, sure, but he may not score the goals to help Bilic raise West Ham's profile even further, after the Irons finished seventh this past season, having threatened to qualify for the Champions League.