The 23-year-old has been in sparkling form for Spurs this season, scoring 15 Barclays Premier League goals including a spectacular winner in Monday's 3-2 win at West Ham.
Bale's stock has risen to such an extent he has been labelled 'world class' in some quarters, but Lineker reckons such comparisons will only serve to heap pressure on the Welshman when he should just be allowed to develop naturally.
"He's massively talented," the 52-year-old said. "He's making such an impact on games on a relatively regular basis and has been doing for quite a while, but the frequency is becoming more. He's becoming more influential in every game.
"The reason I say it's bit unfair to compare him is that they (Messi and Ronaldo) are probably two of the - if not the - best players we've ever seen - certainly the best two of their generation.
"The way football evolves, obviously players get fitter and stronger and quicker, etc, so therefore they're quite likely the best two players we've ever seen.
"So it just puts a little bit of a burden on someone. You know what we're like in this country - we'll build him up, build him up and then if he has a bad spell of three games we'll be saying, 'he's no Ronaldo, he's no Messi' when no-one ever really should have said it in the first place.
"If we look back in three or four years' time and he's performing like he is now... He's performing like Messi and Ronaldo do every week at the moment, but can he sustain that? It's a big ask.
"For me he's certainly the best British player around at the moment, and that's probably where it should stay. We shouldn't start saying he's the best in the world or even close to it at the moment."
While Bale is blossoming under Spurs boss Andre Villas-Boas, it appears a rather less settled ship at the Portuguese's former employers, Chelsea.
Rafael Benitez earlier this week hit out at those who appointed him for giving him the title of 'interim' manager, and at the club's fans for their constant jeering.
Lineker, speaking at the launch of Walkers' home-grown range which sees them introduce the use of ingredients sourced from British farms and producers, said: "It's all gone a bit messy.
"He obviously wasn't an ideal fit in the first place and the fans don't seem to want to take to him. He probably knew a bit of that when he joined, and the interim perhaps he would have known about.
"I suppose he's got a point, but I'm not sure it does him any favours to voice it.
"I guess the position looks more and more untenable by the day. But at the same time I can't see there's any point whatsoever in bringing someone else in now, just until the end of the season, because they're obviously going to appoint someone then anyway so I think it's probably best for all concerned if they just get on with it and support the club and support the team."
Lineker, meanwhile, is lending his own support to former Tottenham and England team-mate Paul Gascoigne, who is currently spending time at an alcohol rehabilitation clinic in Arizona.
"I know that when he first went over he had a bit of a reaction to coming off whatever he was on, and he was in intensive care for a while," the former striker said.
"I now know he's back in the clinic, getting the treatment, and beyond that I've got no news. Hopefully no news is good news.
"There's a massive amount of affection for Gazza right around the country, and hopefully he can take encouragement for that and use it as a motivation to get better because it's got to come from him - we all know that. He's got to really want to do this and hopefully find a reason to do it."
Lineker was recently joined by his father, Barry - a former fruit and vegetable market stall owner - for a road trip across the United Kingdom to sample the home-grown produce that is going into Walkers' new flavourings.
"It was good fun, going round various places with my dad," he said. "It was nice to spend a bit of time with him. We both like our sport, so there's plenty to talk about!"