Hayman, widely regarded as the World's leading tight-head, made two appearances against the Lions in 2005.
Now it has been suggested that negotiations have taken place between his representatives, his club Toulon and the New Zealand Rugby Union about a three-month contract that would allow him to play for the All Blacks once again during the World Cup.
Toulon owner Mourad Boudjallel recently said he would not stop any of his players participating in September's showpiece event.
"Of course I am ready to let him go on condition that he comes back after the World Cup," said Boudjallel.
The Midi Olympique have suggested that before the end of last year, NZRU medical experts requested information about Hayman from Toulon.
The paper reported that Hayman was confussed by the approach as he is contracted to the French club not the NZRU.
But it has been suggested that Hayman or his representatives have replied in a positive manner, saying only that it would be necessary to find a legal agreement.
Hayman is optimistic about his form but brushed aside suggestions that he is the World's best tight-head.
"All that is not true," he said.
"But it is true to say that I am getting better and better in this team.
"Without doubt I have progressed in the last six months and notably in the scrums. Technically, I have learned 'the vice' and that is good because I never thought I could do that."