Pardew is believed to be the Potters number one target for the position vacated by Steve Cotterill.
Stoke, promoted to Division One at the same time as Reading, currently have first team coach Dave Kevan taking charge of the club on a carertaker basis.
Steve Cotterill sensationally resigned from his duties after just five months in charge this week. The ex-Cheltenham boss has since linked up with Howard Wilkinson and become Sunderland's new assistant manager.
Royals boss Alan Pardew, and eight members of his backroom staff, face an uncertain future as they will be out of contract next summer.
It is thought that Pardew, rated as one of the best young English managers, would be willing to head up North to join a club of similar size with similar ambitions if he can get a good contract offer.
A statement from Stoke's Icelandic chairman to the club's official site indicated that the club have already begun the search for their new manager.
"We have already had a number of applications - the selection process has started," read the statement.
"We want to appoint a new boss as soon as possible, however, we want to ensure that we make the right appointment.
"We must be sure that we have the right person for the job, if we need to take time in finding the right person then that it what we'll do."
Meanwhile, speculation suggests that if Ipswich fail to appoint Ronnie Moore as a successor to George Burley they will turn their attentions to Reading's currently in demand boss Alan Pardew.