The Irishman holds the Potters record for the most consecutive games scoring a goal, with four.
Shaqiri has scored in Stoke's last three games - including a wonder-strike last weekend against Leicester City - and Conroy is hoping the Swiss maestro can emulate his success of 1968/69.
"I hope he does it," says Conroy, "because if he does it means we've got a chance of getting a result at Southampton.
"I've always believed that records are there to be broken, so hopefully he doesn't just equal it, but also goes on to break it. We certainly need his goals.
"I must admit I was totally unaware of the record, but it just goes to show that some of us old timers could set a few records.
"Shaqiri has really come to the fore now, hasn't he? He's now the number one with Marko Arnautovic gone and I think he feels that responsibility and has the strength to carry that burden."