Martinez, who has spent pre-season on trial with the Bucks, joins the club as the second goalkeeper to work alongside Jasbir Singh.
The 24-year-old numbers Solihull Moors, Bedworth United, Hereford United and Tividale.
Crewe-born Marsh (pictured) joined Liverpool from Wrexham at the age of 14 where he progressed through the Reds academy.
Although he never made the senior team, Marsh spent several years as a regular in the Liverpool under-21 team and trained with the first-team on several occasions.
He also spent a spell on loan at Sheffield Wednesday and then joined Chester FC in November 2016.
Bucks` boss Rob Edwards is also working on several other targets as the Bucks bid to kick-off the new season away to York City on Saturday.