By that time, Mauger will still only be 30 with a few years of top-level rugby still possible.
Mauger is vastly experienced for a 25-year-old, having been capped while a teenager in 2001.
He also holds a French passport, which is an added bonus for a potential move to England.
Thompson said: "It is very much a work in progress. Leicester have expressed an interest and we know that a number of other clubs are interested in talking to Aaron because he is playing very good football.
"But he will only be 26 after the next World Cup. He might be able to squeeze through to another World Cup.
"He might want to sign an extension with the New Zealand Rugby Union. He's not ready to make any decisions. It's too early for that.
"From the player's point of view, it would be better to wait until after the World Cup but in terms of the clubs' planning, they would want to get things done earlier, in February, March next year."