The Manchester City boss is understood to have told his board the brilliant Belgium winger is one of the few players that could take his squad to the next level.
The newly-crowned Premier League champions have earmarked quality over quantity this summer and Hazard's name is being continually mentioned in the corridors of power around the Etihad Stadium.
City are understood to be keenly observing his present contract negotiations at Stamford Bridge, with the dynamic 27-year-old having less than two years left on his present agreement.
Real Madrid are making their own power moves behind the scenes, with the Citizens being told the Spanish giants are willing to pay Hazard £400k-a-week - £19.2m a year - to force through a move to the Bernabeu.
Guardiola, however, believes Hazard could be tempted by the prospect of playing under him and also linking up with international team-mates Kevin De Bruyne and skipper Vincent Kompany.
City know Chelsea would be highly reluctant to sell to a domestic rival but the cash is there to make a £150m bid for the right marquee addition, in conjunction with meeting any huge personal demands.