The Bolton Wanderers boss has worked under a tight budget and difficult circumstances to bring them back into the Championship at the first time of asking and that has brought him to the attention of Leeds owner Andrea Radrizzani.
Leeds are meeting candidates who could succeed Garry Monk this week with Alan Pardew the bookies' favourite while Claudio Ranieri is not in the running at this stage and is expected to speak to Crystal Palace.
Parkinson, 49, won the League Two play-offs with Bradford City in 2013 and took them to the League Cup final and quarter finals of the FA Cup.
He took over at Bolton in 2016 following their relegation to League One and guided them back into the Championship after finishing runners up to Sheffield United on 86 points.
Bolton would demand compensation should any formal approach arrive for Parkinson though the club remains in a precarious financial position.
Parkinson has been working under a transfer embargo, dealing in loans and free transfers for players and that has yet to be lifted ahead of an important summer.
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