Bosses at Marsh Ltd identified the pair and have started an investigation.
An insurance industry insider said the man was desperate to save his senior management position.
"He's fighting tooth and nail to stay," the source said.
"There are a lot of legal difficulties that Marsh are having to go through, and they are going to take their time.
"But [the man] is hoping that he can return in some capacity to a job that he loves."
But another source claimed that Marsh - horrified by the high-profile incident - wants him out.
"The question is, can the guy get another job without having to expose his past error."
The female employee, understood to be in her 20s and recently engaged, was not at her Christchurch home yesterday and did not respond to messages.
Her ex-fiance has come out in her defence to describe her as a "a really nice person, she never made any mistakes" and say that it was a sad situation "for everyone involved".
The man's wife, who allegedly found out about the affair after seeing it on Facebook, is said to be distraught over the incident.
A neighbour of the family, who wished to remain nameless, said only the man had been around this week.
He appeared to be home alone all day yesterday.
"The wife and kids haven't been about and he's been keeping a very low profile."
Employment law experts say it's possible that the couple could lose their jobs over the incident.
Privacy Commissioner John Edwards said it was unlikely they would be able to sue for breach of privacy.