A memo from president-elect Colin Carter to club directors that detailed records highlighting Thompson's phone and SMS contact with Essendon was revealed in the Herald Sun on Thursday.
A disappointed outgoing president Frank Costa said the Cats would look into how the confidential email found its way into the public arena.
"I'll be having a chat to Brian Cook naturally, because he's the man who runs our club, and runs it very well," Costa said on SEN on Thursday.
"We'll carefully think about if we can find out how it was released. If we can find out how it was released, we will take the necessary action.
"That sort of thing hasn't happened before in my time at the club; a confidential email from one board member to another senior member at the club hasn't got out like that.
"For it to get out like that is very disappointing but we can't do anything about it."
Costa said he couldn't understand the motivation of the person who passed on the information that revealed Thompson was in talks with the Bombers as early as July this year.
"We like to work in an honest way amongst ourselves and if one of the board members sends a confidential note through to others to express a point of view or a thought, normally that's where it should stay," he said.
"I don't know whether it's the heat of the moment with the Mark Thompson scenario that's caused somebody to leak this document ... I don't know, but we are disappointed."
Costa was in Europe with club CEO Brian Cook last month in a trip that included the International Rules Series in Ireland when they were made aware of the findings of the internal investigation into the phone records.
"Our football department was looked at pretty carefully by the administration of the club, and these phone records, because we pay the bills naturally, came to light," he said.
"That was disappointing too. It was supposed to be a private document, and it was supposed to stay private and in-house, and it hasn't and we'll deal with it now as we go along.
"This doesn't help anyone in the sporting world. It doesn't help Geelong and it certainly doesn't help Essendon."
The Cats were made aware of the announcement of Thompson's impending appointment at Windy Hill before it was made public on Wednesday.
Costa said there was no lingering bad blood between the two clubs despite the poaching of both Thompson and assistant coach Brendan McCartney in recent times, and he appreciated the early notice of Thompson's appointment.
He also said the focus for Geelong was now where it was headed in 2011.
"Unfortunately, we've lost some very strong names who were a very important part of Geelong over the last several years, Mark Thompson and Gary Ablett," he said.
"That is history now and we've made our moves going forward and I think Geelong has a pretty exciting future going forward.
"These things hit the news and you have to answer questions."
