The 26-year-old is coming off a difficult season with the Jets, which saw him temporarily demoted from the starting lineup.
Garcia played under new Jets offensive coordinator Marty Mornhinweg during stints at the San Francisco 49ers and the Philadelphia Eagles.
Sanchez told the New York Daily News: "It's great. Jeff sounds like one of those guys that keeps his old playbook and is still really into it.
"He really speaks the language of that West Coast offense. It's nice to hear the schematic side, but also to hear what people think about [Mornhinweg]."
The Jets missed out on the playoffs, finishing third in their division with six wins and 10 losses during the regular season.