However, Price gave no further details.
"That's all I want to say at this time," Price said in a text message.
Price, 50, completed his fourth season as Reds pitching coach in 2012 and it was a strong season for his staff.
Only the Reds and Giants this season had all five of their starters make 30 starts. The last time it happened was the 2003 Mariners, who had Price as their pitching coach. Cincinnati also had four starters reach 200 innings and needed a sixth starter only once this year because of a doubleheader.
The Reds' bullpen led the Majors in relievers' team ERA. Price has also helped develop Johnny Cueto into a rotation ace, and helped turn Aroldis Chapman into a closer in the midst of the season. Cueto won a career-high 19 games and Chapman recorded 38 saves after taking over as closer on May 20.
Price interviewed for a previous Marlins managerial vacancy before he joined the Reds in 2009.
Miami interviewed former catcher Mike Redmond on Wednesday. Redmond is widely reported to be the frontrunner. The Marlins dismissed Ozzie Guillen on Tuesday after only one season as manager.