Henry stood down as All Blacks coach earlier on Tuesday, nine days after leading them to the World Cup crown on home soil following an 8-7 victory over France.
The 65-year-old, who spent eight years in charge and ended with a record of 88 wins from 103 Tests, is in talks to stay on with the New Zealand Rugby Union as a "coach mentor" but also hinted he would consider a move to the northern hemisphere if the deal was right.
Reports last week suggested Henry was eyeing a role with England but he told Radio 5 Live this morning: "There was a wee bit of a stretch in the article.
"I would like to spend a little bit of time, not a long time because I have important family over here (in New Zealand), but a little bit of time assisting if there is a demand from a club or from a union in Europe over the next few years."
Asked whether the sporting challenge or the salary would be the determining factor, he added: "It's a bit of both to be frank, blatantly frank.
"If you are going to get involved in a club in Europe you can only do one club, that's important, and I haven't got a lot of time due to things in have to do in New Zealand.
"It would be stimulating and challenging but we will see what happens."
Henry also backed Martin Johnson to remain as England coach despite the team's shambolic World Cup campaign, which flattered to deceive on the pitch and was littered with disciplinary breaches off it.
He said: "I know Martin reasonably well as he was captain of the Lions in 2001 and he was a fabulous leader. I'd imagine he's still the same character, people don't change.
"Often we shoot our coaches because they haven't got the results but they remain the best people for the job. If Martin is the best person for the job he should be re-appointed."