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.
Gilbert has released a new line of rugby cleats. The Gilbert Virtuo 8S is part of the exciting new product. Check it out.
The Barbarians are one of the top invitational rugby sides with a long history and classic rugby jersey.
The Nike Tiempo is a solid rugby cleat and one of few styles still made from full-grain natural leather.
The Lions get ready for their matches with this green training jersey. It's what the players wear. Get in the Gear!
A cool looking all black rugby cleat with the high performance adidas is known for. Get in the Gear!
Wear the crest of the British and Irish Lions on your t-shirt. A great look for the summer.
The Lions are ready to get their Australia tour underway. They arrive in Perth on Monday.
The New Zealand All Blacks training jersey for 2013/14. Get in the Gear!
The USA Rugby Pro Alternate rugby jersey is perfect for any fan of the Eagles. Get yours to wear during the summer Test matches.
The NEW All Blacks 2013/14 jersey has arrived at World Rugby Shop. Dare to wear the colors of the All Blacks.