The deal would keep the Angels in Anaheim through the 2020 season.
Shaikin reports that the Anaheim City Council is expected to consider the stadium lease's one-year extension on Tuesday.
In October, the Angels opted out of a lease that would have required them to play at Angel Stadium through 2029.
The Angels have reportedly considered new stadium options in Los Angeles, Carson and Irvine. However, Tustin has emerged as a top candidate city due to its "proximity to [the Angels'] current home and fan base."
The Angels have occupied Angel Stadium since it opened in 1966. It's the fourth-oldest venue in the major leagues.