Hazard is happy at Stamford Bridge, but Madrid feel that they can make an offer to convince Chelsea to sell the Belgium international as the European champions look to add another galactico to a squad that already contains Cristiano Ronaldo and Gareth Bale.
Chelsea are expected to spend heavily themselves this summer, with Alexis Sanchez, Romelu Lukaku and Alvaro Morata identified as just three of the club's targets.
Ballack, who spent four seasons at Stamford Bridge, thinks that new signings may help to show the club's ambition and convince Hazard to stay in west London.
"Any club in the world wants to have him," said Ballack, speaking on behalf of BT Sport to Goal. "If Real Madrid wants to spend so much money then that shows how good he is but he has to make sure he knows what he has at Chelsea.
"If we talk about winning the Champions League, of course, Real Madrid is ahead because Chelsea aren't in the competition yet. It could be a factor for a player to know, that his club will spend, to sign those two or three players [to get to the next level].
"To show their existing key players, to see that they can be happy with that squad, right now [and trust] the squad to prove what they can do. That's something that he should look at as well.
"He is a superstar in that team and, of course, Chelsea is always a team that looks to win the Champions League as well. The club always looks to make sure that the club is strong enough to achieve that target. If you are a main player and a key player in that team, that's something you will think about."
Hazard went on a 356-day goal drought in the Premier League last season, but he is back to his best and is one of the front runners to win the PFA Player of the Year award. Ballack thinks that a move to Real Madrid may not guarantee success for Hazard.
"He had a difficult year last year where he seemed at times to not be as motivated," Ballack, who retired in 2012 after an illustrious career which saw him win titles at Chelsea, Bayern Munich and Kaiserslautern, added. "He didn't enjoy his football that much compared to this season. It looks like that watching him on the pitch.
"If you fight for years to be in that position and you want to make a move, especially in this case to Real Madrid, everything would start again new for him. Of course, [he can do it] he has that quality, but next to him will be one, two, three of a different calibre.
"He will have to fight for his place again in that team. We know the history of players at Real Madrid and things are not easy at that club. It is a fantastic club though and I can't give him advice, he must decide it. There will be money involved for the player, from the clubs, everyone will have to be happy from that side [for it to happen]."
Meanwhile, Ballack will be attending Chelsea's game Manchester City at Stamford Bridge as part of his work with British broadcaster BT Sport and he believes that the upcoming match may bring lots of goals.
"It is a big match with different expectations [for both teams]. Chelsea are leading the league and they want to protect first place, especially after defeat at the weekend, they want to prove again that they are right at the top of the league.
"Manchester City are fighting for the Champions League place, that's a really tricky game for both. They are two fantastic teams with a lot of fantastic individual players, so there will be a lot of quality on the pitch and hopefully we will see some goals and some offensive football."
Watch Chelsea v Manchester City live on BT Sport 1 on Wednesday 5th April from 7:15pm. BT Sport is your home of unmissable football. For more info, visit btsport.com/football