Gascoigne has been admitted to a treatment centre in the United States after he started drinking again.
The 45-year-old is reportedly receiving financial support from former Spurs team-mate Gary Lineker and celebrity friends Chris Evans and Piers Morgan and Tottenham have offered to help their former midfielder through their trust.
"The club is helping with the situation through the Tottenham Tribute Trust," said Villas-Boas.
"I think it's extremely sad for a player who represents so much for Tottenham's history. Tottenham have made themselves available to help the situation. Hopefully Gazza can recover."
Gascoigne, who played nearly 100 times for Tottenham after joining them from Newcastle in 1988, has suffered from alcoholism for large parts of his life.
He looked in good health when he was guest of honour for Tottenham's game at one of his other former clubs, Lazio, in November, but he was pictured looking worse for wear last weekend at an event in Northampton.
His agent admitted following the publication of the pictures that Gascoigne had started drinking again.
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