"It doesn't affect our search process at all," Burke told the paper.
"We have a time-frame we're going to follow. That means if a candidate comes off the list we simply proceed to follow our process. Our expectation is we will not receive permission to talk to at least a couple people on our list until after the Draft, and if that's the case, we will wait until then."
The Flames had approached former Dallas Stars GM Joe Nieuwendyk about taking over as GM of the Flames, but he rejected the position.
It's unclear who else the Flames are targeting, though the Sun suggests Canucks Assistant GM Laurence Gilman could be in the running.
Multiple published reports have also linked Toronto Maple Leafs Vice President of Hockey Operations Dave Poulin and Vice President and Assistant GM Claude Loiselle to being in the mix for the Flames' vacancy.
Philadelphia Flyers Assistant GM Ron Hextall is also a hot commodity, being linked to several clubs, but after leaving the Los Angeles Kings for the same role in Philadelphia, the belief is that he will one day take over as GM of the Flyers once Paul Holmgren moves on.
Tampa Bay Lightning Assistant GM Julien Brisebois may also be given consideration.