Carvalho has played just 96 Premier League minutes this season
Carvalho has become frustrated with his lack of action at Brentford since his £27.5million move from Liverpool last year and is keen to pursue a move away, either on loan or permanently.
Any potential loan deal would include the option to make the move permanent, with Carvalho adamant he wants to leave in January rather than waiting until next summer.
The 23-year-old, who has started just four Premier League games for Brentford, rejected a move to Lyon in the summer to stay and fight for his place under Keith Andrews.
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But, despite enjoying a strong personal relationship with Andrews, Carvalho has played just 96 Premier League minutes this season and is now actively seeking a move away from the club.
Carvalho asked to play for Brentford’s B team against Luton Town last Tuesday in order to gain match fitness, scoring twice as Sam Saunders’ side coasted to a 6-1 victory.
Andrews has previously said that he has high hopes for Carvalho, but left him on the bench during last week’s wins over West Ham and Liverpool.
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Carvalho, who is the sixth most expensive signing in Brentford history, has struggled for minutes under successive managers.
Injuries, including a dislocated shoulder that required surgery in March, have contributed to his lack of minutes, but he has become increasingly frustrated by a lack of opportunities.
Lyon, Stuttgart and Strasbourg are interested in the midfielder, who is not expected to be short of options should he depart Brentford in January.