Warner was signed on a six-month loan deal from Cardiff last month to cover for Mark Crossley and Jaroslav Drobny, who are both recovering from knee injuries. The 31-year-old's arrival was intended as a temporary measure, but his outstanding performances could see him land a longer stint with Fulham.
"Tony is a big guy and has great presence, which is a good start for a goalkeeper. He makes good saves. His kicking wasn't great at Blackburn but everyone can go through that," said Coleman.
"The most important thing is that Tony has a lot of confidence in his own ability. He doesn't settle for second best - you can ask our defenders that.
"He's been great on the pitch and in the dressing-room. I knew he was a good goalkeeper but he's really impressed me with his attitude. There's every chance he can stay if he keeps it up."
Another goalkeeper, David James, is being tipped to regain his England place by his Manchester City manager, Stuart Pearce, in time for next summer's World Cup.
Sven Goran Eriksson dropped James for the double-header with Wales and Northern Ireland following the keeper's abject failure in the humiliation by Denmark last month.
James responded to the 4-1 defeat with the startling admission he had not prepared properly for the game.
Although the allegation could have been levelled against virtually all Eriksson's squad in Copenhagen, James paid the price for revealing his lack of preparation so publicly. With Robert Green and Chris Kirkland vying to act as understudy to Paul Robinson, many feel the 35-year-old has played his last game for England.
Pearce is not so sure. He has been hugely impressed by the way James has responded to the latest setback, and his initial save to deny Ruud van Nistelrooy during Saturday's Manchester derby at Old Trafford is likely to be one of the best seen all season, even if Van Nistelrooy tucked home the rebound. Pearce has already seen enough on the training ground to know James is intent on reclaiming his England spot.
"David has never let me down and he has a chance of getting back into the England squad if he keeps playing like that," said Pearce.
"If you are going to be left out of the England squad, it is better to happen a year before the World Cup than a month before - then he would have had no chance."Reuse content