Gallardo had a week after Friday's offer to accept or decline.
Texas did not make a qualifying offer to free agent Colby Lewis, but can still negotiate with the right-hander.
If Gallardo declines the offer and signs with another team, Texas would get an extra pick at the end of the first round in the 2016 draft.
Gallardo was 13-11 with a 3.42 ERA in 33 starts last season. It was his seventh consecutive season with at least 30 starts and 180 innings pitched.
The Rangers also Friday reinstated ace right-hander Yu Darvish from the 60-day disabled list after he missed all of last season following Tommy John surgery.