Rotherham boss Ronnie Moore has already turned down an £850,000 bid by the Welsh side - back in the second tier for the first time in 18 years.
But after a performance that impressed both Moore and Cardiff boss Lennie Lawrence a fresh offer could be in the pipeline closer to the £1million asking price by the Yorkshire club.
Said Moore: "Alan Lee proved why Cardiff want him so badly. He murdered their two centre halves - they were hardly in the game today.
"But at the moment he is still a Rotherham United player and that will not change until they make another move.
"I thought the team were brilliant today, especially considering the heat. You could not fault our effort and commitment. The only problem was our finishing - we were not clinical enough.
"If we carry on playing like that for the rest of the season we will not have any problems. If it had been a boxing match they would have thrown in towel long before the end.
"If we had taken our chances we could have had four or five goals."Cardiff boss Lennie Lawrence admitted: "Lee was a real handful for us but I don’t want to say anything more.
"It was a good point for us but we learnt today that there are no easy games in the first division, it was very tough."Rotherham had the lion’s share of chances and Lee went close with a string of impressive efforts.
An early header was blocked, another effort two minutes before half time was a fraction over the bar and another power header in the dying minutes was well saved by keeper Neil Alexander.
Cardiff's best efforts came from Robert Earnshaw who saw one chance well saved and another drift just wide.