Sir Clive Woodward announces his 44-man squad for the tour of New Zealand on April 11 and hooker is proving to be a problem position, with the likes of Mefin Davis and Shane Byrne having staked their claim during this year's RBS 6 Nations championship.
But former Ireland captain Wood, who toured Australia with the Lions in 2001, believes England and Northampton front-rower Thompson should be first choice.
"My choice would be Steve Thompson, if his throwing improves," he told the Western Mail.
"Mind you, I'm not the man who should be talking about throwing because I was not the greatest.
"However, even I can tell Thompson's throwing looks a bit uncertain at the moment.
"I think he could do with losing a few pounds and getting a bit fitter, but I am sure that he can get fit quickly during the tour.
"When he is at his ebullient best he makes a nuisance of himself and carries the ball so well."