The two London clubs also face competition from Manchester United for the Spain international, who is in the final 18 months of his contract and could be available on a cut-price deal in the summer.
Raya has impressed for Brentford since their promotion to the Premier League and the 27-year-old has been a key part of the Bees side who sit eighth in the table.
Chelsea are targeting a new long-term No.1 and are willing to offload Edouard Mendy or Kepa Arrizabalaga.
David Raya is one of the best goalkeepers in the Premier League.
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It seems more likely that Mendy will be sold, given that he has been unable to agree a new contract after rejecting an offer from the club.
The 30-year-old is one of the lowest paid players in Chelsea’s squad and has attracted interest from AC Milan, Monaco and Nice.
Talks over a new deal are not due to resume until April or May, when more opportunities are available for the Senegal goalkeeper.
Tottenham, meanwhile, are making a long-term succession plan for captain Hugo Lloris and are also interested in Atletico Madrid goalkeeper Jan Oblak.
Oblak is ready for a move to the Premier League, but he would cost a lot more than Raya.
Source: Chelsea FC to rival Tottenham for Brentford goalkeeper David Raya