The new playing surface might be installed in time for Wales' expected friendly against Northern Ireland on Thursday, 24 March.
The surface has deteriorated recently, prompting criticism from Cardiff's players and manager Russell Slade.
"We'll see if there's a period we can maybe do something about it because it's not an easy surface," said Slade.
"There are certain companies who will get it down in a very quick period of time if you need to do something, but it will be a financial decision for that.
"We're talking about that with [Cardiff chief executive] Ken Choo and Wayne Nash, the stadium manager.
"Wales also like playing here so it will be probably beneficial for both of us if we get the right decision. All of us are talking."
The Cardiff City Stadium pitch - a mix of natural grass and synthetic fibres - was set to be re-laid last summer but those plans were put on hold because of Wales' match against Belgium in June.
Heavy rainfall during the winter has seen the turf cut up badly, with the previously lush, green surface becoming muddy and coarse.
It looked in particularly bad condition during Cardiff's FA Cup third-round defeat by League One side Shrewsbury on Sunday.
"I'm not making an excuse because the surface was the same for both teams - but we want to move the ball quickly but sometimes we're having to take three touches instead of two," Slade added.
"There wasn't the work done on it in the summer that there had been previously. There wasn't a period of time big enough for us to take the top off and start again.
"Sometimes you can leave it an extra season and the pitch is OK but, when you get a winter in terms of the rainfall we've had, it's made it very difficult."