Hazard's contract at Stamford Bridge expires at the end of next season and this month he said he has made a decision about his future , though he did not offer any further information.
The 28-year-old has been heavily linked with a switch to Madrid, a path trodden by former Chelsea team-mate and Belgium colleague Thibaut Courtois in the close season.
Ex-Manchester City striker Mpenza believes heading to the Santiago Bernabeu would enable Hazard to take his career to new heights.
"I think he wrote a page in Chelsea's history book and now he has to try to go somewhere else," Mpenza told Omnisport.
"A player always wants to move to another team to improve. Real Madrid won three Champions Leagues [in a row], and Hazard hasn't won it with Chelsea.
"If he wants to improve, he can go to Madrid to become stronger."
Mpenza was speaking ahead of Manchester City's clash against Schalke on Wednesday - another of his former teams - in the Champions League last-16 tie, the first leg of which takes place at the Veltins-Arena on Wednesday.
He has warned City not to underestimate the threat posed by Schalke, however, he believes Pep Guardiola's side are the favourites to retain the Premier League title due to Liverpool's history of struggling against teams beneath them in the table
"We always try to go through, but we failed. This year it's a very tough game against Schalke. People are saying that we are favourites, but it's football, we never know," said Mpenza.
On the domestic battle with City and Liverpool locked on 65 points at the summit , he added: "It's possible [City will win the league]. Now they're tied with Liverpool, but Liverpool are always in the race until the end for the past two-three years.
"And I think City could win again this year because they have a lot of experience … and Liverpool has been losing games they shouldn't lose in the final stretch in the past.
"So I think City has an advantage when it comes to winning the league."