Price addressed the report with local media on Monday morning.
"In this business, a lot of people don't get this opportunity," he said. "I'm really grateful that they're sticking with me to see this thing through."
Cincinnati (58-79) is in last place in the National League Central and while there Has been some improvement in stabilizing the lineup and developing the club's pitching prospects, the Reds are still a ways away from declaring an end to their rebuilding process.
Still, Price, general manager Dick Williams and team owner Bob Castellini have remained on the same page in terms of the rebuild and the players have bought into the process.
Price believes he has been evaluated fairly by the organization. He was informed in July that he was coming back next season, although nothing was announced formally by the club.
"You should get what you earned," Price said. "Since I've been the manager here, we haven't been real competitive. That shouldn't put me on sound footing as the manager.
"What should is that from 2017 to 2018 we make significant improvements. I've got to just do my job. If I keep it, if I don't, that's in the hands of somebody else."
Price, who spent four seasons as the Reds' pitching coach, is 266-357 (.427) since taking over as manager.
For the better part of those four-plus seasons, the Reds have been in rebuilding mode centered around a stockpile of young arms. Cincinnati ranks among NL leaders in several offensive categories and are among the top defensive clubs in the league. But myriad injuries to the starting rotation and constant movement of young arms to and from the minors has slowed the rebuilding process.
The recent emergence of young starters Luis Castillo, Robert Stephenson, Sal Romano and Tyler Mahle has the Reds seeing light at the end of the tunnel.
The Reds began a three-game series on Monday afternoon against second-place Milwaukee at Great American Ball Park.
"The players have stayed together," Price said. "The clubhouse is a good place. The young guys are turning the corner in the rotation. We've got a good foundation to do some really good things here."