The All Blacks' World Cup-winning coach has been linked with a role at Twickenham, either in a short-term caretaker capacity for the Six Nations or as Johnson's permanent replacement.
Henry, 65, is contracted to the New Zealand Rugby Union until March 31, which is after the Six Nations, and admitted he would be interested in working in Europe.
However, the former Wales coach says he would prefer a part-time consultancy role with a club.
"I want an involvement in the game, mainly in an advisory capacity," Henry told WalesOnline.co.uk, when asked about his future plans.
"Hopefully some people think that might be beneficial to their particular situation.
"I'd like to spend some time in Europe but I want to live in New Zealand. Our kids are there and we have five grandchildren. I think it is important we are there.
"I can see myself being in this part of the world for perhaps 10 weeks a year.
"I'd like to be able to contribute and enjoy that contribution. Hopefully it may be beneficial to a club in this part of the world."
Henry, who is in Britain to coach the Barbarians against Australia at Twickenham next Saturday, added he had no concrete plans yet.
"Since the World Cup there has been a lot happening. I'm employed until March 31 next year and hopefully in that time I can get myself organised," he said.
Nick Mallett, the former South Africa and Italy coach, announced just hours after Johnson's resignation that he had turned down the job.
Brendan Venter and Clive Woodward have since confirmed they are not interested, leaving Northampton director of rugby Jim Mallinder as the leading candidate.
Former Australia coach Eddie Jones has expressed an interest and Wayne Smith, Henry's assistant with the All Blacks, has also been linked with the role.
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