The former West Brom boss will hope the surprise loan signing of Tottenham star Keane kick-starts his side's season.
And Keane said in the News Of The World: "I like the way Tony Mowbray sends his teams out. I played against his West Brom teams over the last few years and always admired the way he went about his business.
"They came to Tottenham a few times and almost dominated games, which is very difficult to do at White Hart Lane.
"I respect him as a manager. Obviously I've only been here a few days, but I like his ideas."
Keane added: "Yes, he is under pressure, but there's pressure on everyone. Celtic's a massive club and the expectations are massive. People expect you to win every game so, of course, there's pressure.
"There's pressure on all the players too and we have to go out and deliver. If we give our all between now and the end of the season we have every chance."
Keane, who endured a debut to forget as Celtic suffered a shock defeat at Kilmarnock on Tuesday, hopes to make a real difference at Parkhead before returning to Spurs this summer.
He said: "I think I can help the players. Obviously there are plenty of young players and new players who have come into the club too. I think I can help on the pitch and off it. I think I'm quite good round the dressing room."
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