Li won the 2011 French Open singles title, becoming the first player from Asia to win a Grand Slam in singles. She was also a finalist at the 2011 Australian Open, becoming the first Chinese and Asian player to make a major singles final.
Ramos, fresh from overseeing the club's comprehensive 5-1 demolition of Arsenal during last night's Carling Cup tie, is conscious of the need to bring in added cover for both defence and midfield.
Top of the list is a quality centre-half, as back-up to Ledley King and Michael Dawson, and the Spanish coach has pinpointed Argentinian international Ezequiel Garay as the man to plug Spurs' leaky defence.
Garay, 21, is valued at £10 million by his club Racing Santander and Liverpool manager Rafa Benitez has already expressed an interest.
However, due to the recent turmoil at Anfield, Ramos is hopeful of stealing a march on his Premier League rival and completing the signing before the January transfer window closes.
Tottenham are also in the hunt to sign Spanish international David Albelda.
The 30-year-old Valencia midfielder is out of favour at the Mestalla, reportedly forced to train alone and told he will not be picked for the first team again by new manager Ronald Koeman.
Albelda, who has 46 caps for Spain, said: "I am very attracted to playing in England and especially if the club was in London.
"I am grateful to Tottenham for their interest but I cannot negotiate until I've sorted out my departure from Valencia.
"I'm still waiting for an explanation, for someone to say something. I can assure you that I've never had an argument or incident with Koeman or the president, but one day I was playing and the next day I was out."