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 team that sits eighth in the table.
Chelsea are targeting a new long-term No1 and are ready to offload either Edouard Mendy or Kepa Arrizabalaga.
Mendy looks more likely to be sold, given he has failed to agree a new contract after rejecting an offer from the club.
The 30-year-old is one of the lowest-paid players in the Chelsea squad and has attracted interest from AC Milan, Monaco and Nice.
Talks over a new deal are not due to restart until April or May, when further opportunities may become 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 to move to the Premier League but would cost significantly more than Raya.