The La Liga giants are said to have made Hazard, 26, their priority target ahead of the summer transfer window.
But Ballack believes Hazard could struggle to adjust to life in the Spanish capital due to his personality and the egos at Madrid.
‘Hazard did not have a good season last year and sometimes you don’t really know what happens to players,’ Ballack said on behalf of BT Sport.
‘But it seems to be that he’s a bit of an emotional player who needs support and needs to feel really comfortable with the coach and the team and in his private life as well, so that he can perform.
‘I’m pretty sure if he moved to Real Madrid he would have to fight for that standing again and it would take time because he’s a bit of an introvert.
‘He’s not a player who talks a lot, and Real Madrid, if you see the players they have, it would be a different situation for him.’
Ballack, who won the Premier League at Stamford Bridge, added: ‘He has to decide if he wants to be successful with Chelsea and go into the Champions League, on another level, and help them back to where they were in Europe.
‘They are talking about a lot of money. That’s surely also a factor for a player or a club.
‘But if you speak about football facts, I think he’s in a position where he fights for a long time and he will not have the standing he has now at Chelsea at many clubs in Europe so he has to fight for that and that takes a few years again.’
Chelsea lost their first game in almost three months against Crystal Palace on Saturday to concede three points to their title rivals.
Antonio Conte’s charge will be hoping to respond at home to Manchester City on Wednesday evening.