Rowett left Derby County last week in order to join newly-relegated Stoke, ahead of their season in the Championship.
Republic of Ireland international McClean was also relegated from the Premier League, finishing bottom of the league table with West Brom despite a late upturn in form by the team.
McClean had been a transfer target of Rowett's previously at Derby in January too, but a move didn't materialise.
At the time of the links, McClean said he was largely in favour of a move to the Rams.
He told the Derby Telegraph: "They were second in the Championship at the time and I wasn’t playing as regularly as I’d like.
"I wanted to leave but the same thing happened; the club saying that I wasn’t going anywhere. The usual ‘you’re vital’, but as soon as the window closed, I didn’t play again."
A report on the Mirror's daily transfer live article suggested that the Potters had already tabled a £4m bid for the winger, but West Brom are understood to be holding out for a £6m fee.
Rowett has also been asked to undergo a huge clearout of first-team players from the club, with as many as 15 senior players understood to have been targeted for exits in a mass exodus from the bet365 Stadium.
The likes of Jack Butland, Xherdan Shaqiri and Joe Allen are expected to attract interest during the summer, while big-money signings for Stoke including Kevin Wimmer, Gianelli Imbula and Saido Berahino are all expected to be available too.
Other names being touted for an exit from the club are Ibrahim Affelay, Charlie Adam, Darren Fletcher, Geoff Cameron and Eric Maxim Choupo-Moting.
Glen Johnson and Stephen Ireland are out-of-contract.