Shevchenko, 30, joined the Premiership champions from AC Milan for £30.8 million in May. He has been linked with a possible return to Milan, reports today quoting him as saying that his style of play did not suit Mourinho, and that he was "ready to pack his bags" and go back to Italy if he did not fit in.
However, Chelsea have insisted in a statement that his comments were misinterpreted.
Shevchenko said he had not discussed his future with the club.
Chelsea's Russian owner Abramovich was instrumental in Shevchenko going to Stamford Bridge, where he is on a four-year contract. The popular belief was that Shevchenko's goals and experience would help Chelsea win the Champions League.
The Ukraine international is revered as a hero in Milan, where the Rossoneri have clearly missed his talents so far this season.
In the Premiership, however, he has so far struggled to reach his best form.
Shevchenko himself has now clarified the situation, insisting that he has given only one interview in recent weeks to a Russian magazine called ProSport, and reiterating his commitment to Chelsea.
"I give 100 per cent all the time and I am committed and hungry for success with Chelsea," he said.
"I have total respect for the Chelsea club and fans as well as for football in England and the culture of the country.
"There are always good and not so good moments in sport, that's normal. If that means there is opinion and criticism, I respect that."
In the ProSport interview, Shevchenko admitted that he was unhappy with his start at Chelsea, but denied struggling to adapt to the demands of English football.