Miller visited the Los Angeles Rams on Sunday to better gauge his market value.
The Bears also re-signed tight end Rob Housler on Monday to a one-year contract. Chicago is currently shopping starting tight end Martellus Bennett, who is under contract through 2016.
Healthy for virtually the first time since 2010, Miller emerged as a key playmaker on offense last season with 34 receptions for 439 yards and five touchdowns in 15 games (14 starts).
All five of Miller's touchdowns occurred in the final eight games he played. His 87-yard TD reception at St. Louis in November is the second-longest reception ever by a Bears tight end and is tied for the seventh-longest overall in franchise history.
A week earlier, Miller also made one of the top plays of the season when he hauled in a game-winning 25-yard touchdown catch in the fourth quarter at San Diego.
Prior to his arrival in Chicago, the 30-year-old Miller saw game action with the Jacksonville Jaguars from 2009 to '11.