The two men were detained on suspicion of offences under Section 41 of the Terrorism Act 2000, the force said on Tuesday.
Sources told the that the suspected plot was “fairly imminent” and in the later stages of planning.
Police said searches at properties on Epworth Street in Liverpool and Lancaster Road in Salford had also taken place.
Yom Kippur is considered to be the holiest day in the Jewish calendar.
A spokesperson for the Community Security Trust, which coordinates security for Jewish communities in the UK, said on Tuesday that the suspected plot was “utterly chilling coming so close to the anniversary of the terrorist attack at Heaton Park Synagogue last year”.
They added: “[This] is another reminder of the serious terrorist threat facing Jewish communities in this current time.”