The Swede's contract expires at the end of the year and the runner-up in the Tour's mountains classification is proving attractive to several other teams.
Spanish website Bicicciclismo reported that the 32-year-old had re-signed with Astana however, the rider has refuted the claim.
"I am well advanced in negotiations with Astana, but still no written contract," Kessiakoff told Eurosport.se.
Saxo Bank-Tinkoff is also believed to be interested in his services.
Kessiakoff enjoyed a gallant performance in his Tour de France debut this month, wearing the polka dot jersey on seven stages in a
fierce battle with Frenchman Thomas Voeckler. He earned the red dossard of most combative rider on Stage 8. When his rival secured the mountains classification on Stage 16, Kessiakoff had nothing but praise for Voeckler.
"I'm really disappointed to have lost the jersey but if you look at the way Voeckler took it from me, I could do nothing," Kessiakoff told Cyclingnews at the finish.
"He had a superb race and it seemed like he must have taken every point that it was possible to take today. It didn't matter whether I was feeling good or not - the way he did it, it was just 'chapeau'."
Thank you for signing up to Cycling News. You will receive a verification email shortly.
There was a problem. Please refresh the page and try again.