The position has become a concern for the Italian club after injuries and form issues affected Andrea Cambiaso, while Juan Cabal has also been unavailable with a thigh injury.
Juventus had explored a move for former Argentina international Nicolás Tagliafico during the summer, but the deal depended on Cabal leaving the club and ultimately did not materialise.
Cabal attracted interest from Atalanta but remained in Turin, leaving Juventus with limited options on the left.
The club have therefore identified Raum and Mitchell as potential solutions.
Both players are represented by ROOF and are due to become free agents at the end of the season, meaning Juventus could explore an approach before the January transfer window or wait until next summer.
Raum has established himself as an experienced Bundesliga and Germany international, while Mitchell has become a regular for Crystal Palace in the Premier League.
The England defender has also started the season strongly, including scoring twice against Fulham.
Former Manchester United chief scout Mick Brown recently praised Mitchell’s consistency and defensive ability while recommending him to Premier League clubs.
Juventus believe both players could operate in either of Luciano Spalletti’s preferred systems, with the club alternating between a 4-2-3-1 and 3-4-2-1.
The shortage of natural options on the left has increased the urgency around the position, with Juventus now expected to continue monitoring the market.
A January move could allow the club to address the issue early, although both Raum and Mitchell could also become available as free agents next summer.