Hazard completed an £88 million move to Santiago Bernabeu from Chelsea earlier this summer, as manager Zinedine Zidane continues to strengthen his squad ahead of the new season.
Prior to his switch to Spain, Hazard helped Chelsea finish third in the Premier League last season with 16 goals and 15 assists, while Messi notched in 36 goals and 13 assists for Ernesto Valverde's men in the Spanish top-flight.
While the Argentine star chases his sixth Ballon d’Or triumph, Eto'o is upbeat about Hazard’s chances of winning the coveted individual award now that he is in Madrid.
"Hazard has to win the Ballon d'Or," Eto'o told Radio MARCA and El Partidazo of COPE.
"He hasn't been valued enough but now he's at one of the best teams in the world all eyes will be on him.
"He's close to Messi's level and I hope that he plays Barcelona when he's not at 100 percent."
Barcelona have been linked with a move in trying to bring Neymar back to Camp Nou from PSG this summer.
When quizzed about the return of the Brazil star, who left Barcelona for £222million two years ago, Eto'o said: "If he returns home, it'll be good for the project and the future."