McCarthy was sacked after the Packers lost to the Arizona Cardinals at Lambeau Field on December 2, 20-17.
But according to Adam Schefter of ESPN, McCarthy doesn't want to be considered for any other head coaching vacancy other than the Jets'.
Gase was hired despite going 23-25 over three seasons in Miami, leading to his firing.
Miami faces the Jets twice a year, as both are in the AFC East. In 2013, Manning set the National Football League record for touchdown passes in a season with 55, and any sway from Manning was going to hold weight, especially for a team with a now second-year start quarterback in Sam Darnold in need of further development.
Gase followed coach John Fox to Chicago in 2015 to be the Bears' offensive coordinator.
The Jets did not have a great 2018 season under Todd Bowles as they went a disappointing 4-12.
Instead, the Jets opted for Gase, who has a solid reputation for working with quarterbacks. They both agreed that this marriage would not have worked, as the Jets were not satisfied with the staff, specifically the offensive coordinator that Rhule wanted to bring in to help groom Sam Darnold. "That counts for something".
He's been a collegiate head coach since 2013, first taking Temple to a pair of bowl games in four seasons, then taking over Baylor in the wake of the Art Briles scandal.