The 45-year-old's agent Terry Baker said at the weekend that Gascoigne needed "immediate help" and called on the English Professional Footballer's Association (PFA) to intervene.
"He sounds as if he needs almost a 24-hour watching brief at the moment," PFA boss Taylor told BBC Radio 5 live.
"It seems as if he needs somebody with him all the time just to make sure that he's looked after and is not going to do anything silly."
Taylor said he had spoken to Gascoigne after the PFA paid for the former Tottenham Hotspur, Lazio and Rangers player to attend a detox programme at a well-known clinic for sportsmen suffering from addictions.
"I've spoken to Paul over the weekend, and he's said it's just a blip. But it really is down to him. We just don't want this to be another George Best tragedy," he said.
"He does need a big support system, and he's got it from lots of friends. But there is a frustration that when things look to be improving, it all goes off wire."
Taylor refuted suggestions by former Manchester United goalkeeper Peter Schmeichel on Twitter that the PFA had not done enough to help Gascoigne.
Schmiechel had written: "This is not fun watching. Gazza needs help. Come on PFA & Gordon Taylor, time to step up."
"There isn't a player we've done more for over my time at the PFA," Taylor countered.
"In fact, we've been criticised for doing as much as we have, because he has not made the improvements that some of our other members have."
Former Manchester United great Best died after a long struggle with alcoholism in 2005.
Gary Lineker added that he feared the worst for his former team-mate.
"I can only hope he finds peace somehow," Lineker said on Twitter, "but fear those hopes may be forlorn."