The Atalanta midfielder has been heavily linked with a move to the Premier League with Chelsea his biggest admirers.
However, reports in recent days suggest the 20-year-old is heading to Serie A rivals Roma.
But Roma's director Ricky Massara insists the claims are false.
Franck Kessie is attracting interest from a host of clubs
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No, that's not the case. Kessie is an Atalanta player, a very good player who has received attention from big clubs, but Atalanta have no intention of selling and are holding on tight
“No, that's not the case. Kessie is an Atalanta player, a very good player who has received attention from big clubs, but Atalanta have no intention of selling and are holding on tight," Massara said.
AC Milan are also thought to be keeping tabs on the Ivory Coast international and Kessie's representatives have already held talks with Milan's director of sport Massimiliano Mirabelli.
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But with Kessie's future still uncertain and nothing set in stone, Chelsea are likely to continue their pursuit.
Franck Kessie is under contract with Atalanta until 2021
Antonio Conte reportedly tried to bring Franck Kessie to Chelsea last month
Antonio Conte wanted to bring Kessie to west London last month to bolster his midfield options but Atalanta were reluctant to part with him.
Kessie, who is under contract with the Italian side until 2021, has netted six goals in all competitions for the club this season.