Veteran pitcher Scherzer, 30, is testing the waters of free agency after rejecting a six-year extension from the Tigers reportedly worth $144million in March.
Scherzer's agent Scott Boras recently suggested his client could still make a return to Detroit.
However, Dombrowski believes the odds are stacked against his MLB franchise.
"It is a possibility? I guess anything's a possibility," Dombrowski told MLB Network Radio on Friday.
"I think our odds were better last spring, when we were the only club able to negotiate with him.
"I don't know how your odds get better. Is there any chance? Sure, but I think it's one we're not counting on at this point."