Reports in Turin claim Juve have had a joint 15million euros bid for the players accepted, but Udinese sporting director Fabrizio Larini told Gazzetta dello Sport: "The papers can write whatever they want but nothing has been done yet.
"The only thing that is true is that we have met with Juventus and we have spoken about their interest in our two players.
"Negotiations are at an advanced stage but I reiterate that no agreement has been reached.
"The figure mentioned by the press does not correspond to the truth."
Ghana international Asamoah has reportedly also attracted the attention of Manchester United after another strong campaign while Chilean winger Isla, who sat out the last few months of the season due to a knee injury, is believed to be a target for Inter Milan.
With interest high, Udinese owner Gianpaolo Pozzo insists there is no danger of either player leaving the club on the cheap.
"Our club is not a supermarket," Pozzo told udinese.it. "Our players are precious and they cost a lot of money.
"But if there are important offers from big clubs for our players then I imagine it will be difficult for us to keep them."
Udinese sold Alexis Sanchez, Gokhan Inler and Cristian Zapata a year ago but still finished third in Serie A last season to qualify for the preliminary stages of the Champions League.