The Seahawks also plan to meet with Kansas City Chiefs quarterbacks coach and passing game coordinator Mike Kafka, Fowler adds.
Seattle dismissed offensive coordinator Brian Schottenheimer following its wild-card loss to the Los Angeles Rams.
The Seahawks ranked in the top 10 in scoring in each of Schottenheimer's three campaigns with the team. However, Seattle failed to top 30 points in each of its final four contests this season after eclipsing that mark in all but one of the team's first eight games.
Gase previously worked as the offensive coordinator for the Denver Broncos (2013-14) and Chicago Bears (2015). However, the 42-year-old's teams failed to rank higher than 17th in scoring over his five seasons as a head coach with the Jets and Miami Dolphins.
Kafka joined the Chiefs in 2017. He's been praised for helping turn Kansas City into one of the NFL's most prolific offenses.