It is understood that Potters are still the favourites to sign the shot-stopper after initially being linked with a move earlier this summer.
Whereas Stoke manager Michael O’Neill has made enquiries about Clark, he will have to cut ties with one of the existing members of his squad before stepping up this particular pursuit.
The Potters are currently able to call upon the services of Josef Bursik, Jack Bonham, Frank Fielding and Blondy Nna Noukeu.
Noukeu spent the first half of the previous campaign on loan at Crawley Town and has yet to make a senior appearance for Stoke.
Fielding has also yet to make his bow for the Potters since securing a switch to the bet365 Stadium.
Clark is currently on the lookout for a new club after his contract at St Johnstone reached a crescendo in June.
The 30-year-old recently opted to turn down the chance to seal a move to Dundee United.
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Whilst it would be somewhat of a shock to see Bursik or Bonham depart this summer, Stoke may be tempted to sanction a move for Noukeu or Fielding in order to make space in their squad for Clark.
During the previous campaign Clark managed to produce some assured performances for St Johnstone.
Whereas it could take some time for the shot-stopper to adapt to life in the Championship due to the fact that he has never played in this division before, there is no reason why he cannot eventually go on to make a positive impact for Stoke if they decide to swoop for him.