Newcastle have been unable to agree personal terms with the former Chelsea and West Ham assistant manager, who was a coach at the Tyneside club during Ruud Gullit's spell in charge.
Colin Calderwood left St James' Park to take over as manager at Hibernian a fortnight ago and Clarke has been out of work since leaving West Ham last summer following the dismissal of Gianfranco Zola.
Steve Stone was in the dugout when Newcastle were beaten 4-0 by Arsenal in the Carling Cup but it is unlikely he will be offered the job.
Newcastle United insisted that Clarke was not offered the job but the Daily Telegraph claim: "we have it on good authority that he was at least sounded out about the vacancy".