The Portuguese coach, who has been strongly linked with Everton, has entered negotiations to extend his stay in the Ukraine, according to Sport Witness.
"There's no deadline or fixed date. Negotiations are underway," Fonseca is quoted as saying at a press conference, in response to a question about his contract situation.
Everton are said to be lining up Fonseca as a potential replacement for Sam Allardyce, who has fallen out of favour with sections of club's fanbase.
Previous reports suggest that Shakhtar are willing to pay Fonseca £8m per year to ward off Everton.