Mr Cowen about rumours circulating about the bank.
Mr FitzPatrick also told Mr Cowen about problems with the shares held by the businessman Sean Quinn, who acquired them using risky contracts for difference, known as CFDs.
Taking out CFDs is effectively betting on a share price going up and trying to make a quick profit.
In the book 'The FitzPatrick Tapes', the Anglo boss says: "I told him that (Quinn) had it in CFDs, I think. I am not sure. What I said was what was really happening was that pressure was coming on from the shorters, these guys, the hedge funds, trying to get Quinn."
Mr Cowen also met the board of Anglo for a private dinner at Heritage House on April 24 -- just a fortnight before becoming Taoiseach. He arrived late and Mr Drury introduced him to the other guests.
"Cowen had a gin and tonic and chatted with a group of about a dozen Anglo board members and executives," the book says.
At dinner, Mr Cowen drank red wine and sat with Mr FitzPatrick on his left and Anglo chief executive David Drumm on his right.
"After dessert FitzPatrick asked his key executives to give Cowen a brief update on the lending environment in their various areas."
Anglo's non-executive directors also updated Mr Cowen on how they saw the economy.
Mr Drumm repeatedly spoke about how difficult it was to hold on to deposits and raise new funding in the crisis.
"'David did ask about the NTMA. Anglo wanted (Mr Cowen) to have a word about it placing some of its money on deposit with the bank. He said he'd look into it," Mr FitzPatrick says.
But there was no discussion of Mr Quinn or of the urgent phone call six weeks earlier.
Mr Cowen, Mr FitzPatrick and Mr Drury met for a round of golf on July 28 at the Druid's Glen course in Co Wicklow. According to Mr FitzPatrick's diary, he was with Mr Cowen from 10am to 5pm. After golf, the three ate in the resort hotel.
Mr FitzPatrick insists their discussion had "absolutely nothing to do with Sean Quinn or with Anglo Irish Bank or anything like that".
The authors of the book, Tom Lyons and Brian Carey, note: "It is hard to believe that FitzPatrick and Cowen did not discuss the specifics of Anglo's troubles, but FitzPatrick insists this was the case.
"Uncharacteristically, FitzPatrick refuses to be drawn further on the day he spent with Ireland's leader at a most critical time in the history both of Anglo and the country."