Santos has spent the second-half of the season on-loan with with the Ligue 1 club. Strasbourg are owned by Chelsea's umbrella company BlueCo.
The midfielder scored a last-minute winner in the derby win against Metz, his first goal in European football.
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Santos has started Strasbourg's last eight games.
The London Evening Standard says Strasbourg intend to ask Chelsea about a new loan for 12 months.