Daniels has one year left on his contract. Davis intimated an extension for Daniels would have already happened had the team not been focusing on hiring a new manager.
"I love the organization and I love the community," Daniels said. "It's not really something for me to think about."
The Rangers ended the 2014 season with a 67-95 record and finished last in the American League West while dealing with a rash of injuries. The team made the playoffs the previous seasons.
Daniels had the lead role in the team's managerial search after Ron Washington resigned late this season due to personal reasons. He later said he cheated on his wife and needed time away from baseball.
After naming three finalists for the manager's job on Tuesday, Daniels and the Rangers announced the hiring of Jeff Banister on Thursday. Banister had served as the bench coach of the Pittsburgh Pirates since partway through the 2010 season.
Daniels, 37, has been Texas's general manager since the end of the 2005 season, at which point he became the youngest GM in MLB history at the age of 28 years and 41 days.
After three losing seasons, the Rangers had the team's first winning season under Daniels in 2009 and made the playoffs the next season, eventually falling in the World Series to the San Francisco Giants. The team made the World Series again in 2011, losing to the St. Louis Cardinals, and lost in the AL Wild Card Game in 2012.
Daniels, who received the added title of president of baseball operations before the 2013 season, has engineered several major moves while serving as the Rangers' GM, including the signing of Japanese pitcher Yu Darvish and the acquisition of Detroit Tigers first baseman Prince Fielder.
Daniels has already made one transaction this offseason, informing outfielder Alex Rios earlier this week that the team wouldn't exercise his option for 2015, thus making him a free agent.
- Ben Estes