The Blues are reportedly losing patience with club record signing Fernando Torres, who has managed just 14 Premier League goals since his ?50m move from Liverpool in January 2011.
Although the arrival of Demba Ba earlier this year provided competition for the Spaniard, club owner Roman Abramovich is expected to sanction the signing of a big-name striker in the summer - and Gomez is thought to be on his shortlist.
The Germany international, who scored 41 goals last year, has been usurped by Croatia star Mario Mandzukic this season and could be on his way when Pep Guardiola takes over at Bayern in the summer.
However, should Chelsea look to bring him to west London they will have to dig deep as he is valued at ?36m.
Source: DSG
Source: DSG