Manchester United have been tipped to pursue Perisic, who was wanted by Jose Mourinho a year ago.
Since then, the Inter Milan star’s stock has risen after he fired Croatia to a first-ever World Cup final in Russia last month.
But Stone tweeted: “Told nothing happening re Perisic at the moment.”
Mourinho has cut a frustrated figure during pre-season, fuelling fears United are heading for another campaign of turbulence.
And he used his pre-match appearance today to hit out at Ed Woodward over the lack of transfer activity.
He said: “My CEO [Ed Woodward] has known what I want for quite a long time. He knows what I want.
“I know that he tries his best for me. I still have a few days to wait to see what is going to happen.”
Perisic, meanwhile, has sent Manchester United fans into a meltdown after admitting he would be open to a Premier League switch.
The Inter Milan star has never chanced his arm in English football.
And he said: “I would like to test myself in all of the biggest leagues but the question is will I have the time, I am 29 and working to extend my career as long as I can.
“Yes, I’d like to play in England and Spain but I don’t know if there is enough time left.”
United are set for a defining week.
They have just five days to bring in new recruits.
And they then face Leicester in their Premier League opener on Friday night.