Albert's base salary will be $9.828 million for the 2013 season. He has not signed the tender yet, according to the reports.
Albert and Chiefs can continue to negotiate a long-term extension even after he signs the tender. Kansas City also might choose to trade the tackle.
Sports Illustrated reported Monday that the Chiefs will listen to trade offers for Albert.
The 28-year-old left tackle has played in 73 games for Kansas City, starting in 71.
The Chiefs selected Albert 15th overall in the 2008 draft.