Griezmann is Manchester United's number one target with Jose Mourinho instructing executive vice-chairman Ed Woodward to bring the France international to Old Trafford this summer.
Last week, United appeared to receive a boost when Griezmann said he wanted to leave Atletico to win trophies.
But days later the 26-year-old insisted he wanted to win trophies with Atletico.
And on Friday Griezmann wrote on Twitter: "All the rumours are unfounded. I'm still Colchonero.
"My direction will be established after discussion with my sporting advisor."
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I think Griezmann has made it very clear in his mind that he will remain
Atletico Madrid assistant Juan Vizcaino
However Diego Simeone's assistant coach Juan Vizcaino has expressed his confidence in Griezmann staying.
"I think Griezmann will stay," Vizcaino told Spanish radio station Cadena Ser.
"At this stage, you can misinterpret remarks made by anyone.
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Will Antoine Griezmann leave Atletico Madrid this summer?
"I think Griezmann has made it very clear in his mind that he will remain."
Vizcaino's comments follow those made by Atletico president Enrique Cerezo, who was similarly confident about Griezmann's future.
He told Spanish newspaper Marca: "Griezmann will stay here. Not here at the Calderon, but at the Wanda."