The 27-year-old is a prime target of Tony Pulis's, a report claims.
The report claims West Brom will hand Pulis a £30 million war chest, potentially raised by selling Saido Berahino (wanted by Tottenham).
And Lennon is said to be a prime target of the Welshman's should those funds be made available.
On this occasion, £9m has been quoted as Tottenham's asking price, though, as West Brom are linked to the winger Stoke are also said to be interested in.
Lennon has fallen down the pecking order at White Hart Lane but it remains to be seen whether Mauricio Pochettino wants to keep faith with the 27-year-old.
Should he be allowed to leave Spurs, West Brom is now a touted destination as well as Stoke.