The Leeds Carnegie hooker lost his starting place to Northampton's Dylan Hartley at the start of the autumn Tests but Regan believes the 32-year-old has all the attributes to return to Martin Johnson's starting line-up and flourish in the RBS 6Nations.
"There's a lot of talk about Dylan and he's not likely to get dropped but if Thomo keeps playing well for Leeds and England, when he gets his chance, then he'll be all right," said Regan, a Lion himself in 1997.
"He's got a good chance of getting his shirt back and getting into that team and holding it for the World Cup."
In April 2007, four years after lifting the World Cup in 2003, Thompson was forced to announce his retirement after a serious neck injury. But after seeking new medical advice five months later, Thompson performed a u-turn and played for Brive before linking up with Leeds.
"I remember reading a story when he came out of retirement where he said 'if Mark Regan can play in a World Cup final at 36, then I can'," added Regan.
"And he can. Thomo's been around and he knows what it's like to win a World Cup final.
"He also knows how to perform in the types of conditions you'll see in New Zealand, and England themselves know how to win the tight matches.
"Hartley is a good player but he's too hot-headed. He gives away too many penalties and in the Premiership on Saturday, Leicester took him apart. Mentally, they tore him apart in the lineout.
"Thomo used to get that, nerves during the lineout, but he's addressed that now. And he's got that aggression in his game as well. There's a shortage of good quality hookers in this country but Thomo is definitely one of the better ones.
"If you're playing well in a side that's losing then you'll play a lot better in a side that's winning. It's easier for players at the likes of Leicester to be called on just because they're at the big clubs."