Gase was sacked at the end of the season by the Miami Dolphins after three seasons.
Adam Gase looks on during a game against the New England Patriots at Gillette Stadium in September.
The Miami Dolphins dismissed Gase after going 7-9 during the 2018 regular season.
Dowell Loggains is expected to be named as an offensive assistant with the Jets, sources told ESPN's Jeff Darlington.
Prior to his time as head coach in Miami, Gase was an offensive coordinator with the Chicago Bears and Denver Broncos. The team has a young, promising quarterback in Sam Darnold, almost $100 million available to spend in free agency and the third overall pick in April's draft.
McCarthy was sacked as the Packers' head coach mid-way through the 2018 season.
Mike McCarthy and Matt Rhule were also candidates.
McCarthy, who took over the Packers in 2006, was sacked by the team in early December after it got off to a 4-7-1 start. And if this report is anything to go by, it appears McCarthy views the Jets as that ideal fit for his services.
There are only three head coaching vacancies remaining in the National Football League, with one of them being the New York Jets.
Kingsbury was hired Tuesday as the Arizona Cardinals' head coach.