Celtic keeper Gordon has first-hand knowledge of Keane’s managerial style from their time together at Sunderland.
Keane, now the Republic of Ireland’s assistant manager, signed Gordon for the Wearisde club for a record £9 million from Hearts in 2007.
“He’s hard but fair. What you see is really is what you get,” Gordon told the BBC.
“If he was appointed, I’m sure he would do well and he would be successful.”
BoyleSports, one of Ireland’s leading bookmakers, said it had suspended betting on Keane to be the next Celtic manager on Tuesday morning after seeing “an avalanche of support” for the former Manchester United captain.
Ronny Deila’s sojourn at Celtic will come to an end on Sunday but it is understood the newly crowned Scottish champions are still interviewing candidates and no decision is imminent.
“I know how he liked things to run at Sunderland,” Gordon added. “He was an aggressive player, he wanted to win every match and, from what I’ve seen, he is exactly the same as a manager.”
A number of high profile candidates have been linked with the Celtic job in recent weeks including David Moyes, Paul Lambert, Brendan Rodgers and former managers Martin O’Neill and Neil Lennon.
Liam Glynn, a spokesperson for BoyleSports, said: “We have had to suspend betting on the next Celtic manager after an avalanche of support for Roy Keane over the past 24 hours.
“We couldn’t lay a single cent on original favourite Martin O’Neill over the past 48 hours, it’s all been about Roy Keane and it has gave our traders no other choice but to suspend the market as it now looks like that Roy Keane has been in talks with the Celtic management and things have gone smoothly so far.”