The Eagles only have one senior keeper available at Selhurst Park and Hodgson has been scanning the market for free agents to come in and offer alternatives to Wayne Hennessey.
Cavalieri is a free agent after cancelling his contract with Fluminense and the 35-year-old could be heading back to the Premier League over the coming days.
Hodgson knows the South American from their time together at Liverpool, when he was a back-up keeper, and Cavalieri could well provide cover for first-choice Hennessey for the remainder of the Premier League season.
Uwe Rosler was sacked by Fleetwood following a 3-0 reverse at Doncaster which condemned Town to a seventh straight defeat in all competitions.
Cambridge interim head coach Joe Dunne was pleased with how his side adapted to beat Grimsby 3-1.