In an interview with The Herald, Mr Mather said of the email allegedly sent by a member of Media House: "I do not know anything about that [email] but I have asked people to do some digging on that and come back with a mini-report.
"John Greig is a legend. I have tried on numerous occasions ... to see if he would come back to the club."
The email questioned Mr Greig's intelligence and his contribution to the board. He served on it until the arrival of Craig Whyte, who took the club into administration. Mr Whyte employed Media House.
Jack Irvine of Media House said: "The whole leaking of emails is being investigated by the police at the highest level, so I cannot comment on that."
Mr Mather denied Rangers were running out of money, said high earners were open to wage cuts and added he was having peace talks with Frank Blin, one of a group demanding boardroom changes. He also said Rangers were seeking a prominent chairman after turbulence had "calmed down".
Mr Mather, who has invested some £1 million in the club, was bullish about the Media House contract, saying: "There is a slight misconception regarding Media House. Media House had a contract here that came to an end in August. We renewed that."
Asked if the club was running out of money, he said: "Categorically no."
He also ruled out a share issue, but said talks were continuing over budget cuts. These included discussions with high earners at the club.
He said: "Alistair [McCoist, the club manager] has said he is going to talk about his pay package. We have had discussions on this and these are ongoing. He is very open-minded and positive about change, about addressing that. I have done the same."
He promised that Charles Green, the former chief executive, would not return.
* Ex-Rangers director Dave King has avoided jail and will pay around £44m to South African tax authorities after a case against the Scot was settled.