According to the Mirror, Guardiola has identified the Belgian international as his top summer target after the club missed out on Alexis Sanchez.
The Cityzens seemed to be the favourites to land the former Arsenal man's signature this month after a summer deadline day move collapsed.
However, they were put off by Sanchez's exorbitant wage demands as Manchester United stepped in and were able to complete a swap deal with the Gunners as Henrikh Mkhitaryan went the other way.
Having admitted that last summer's squad revamp affected his ability to sign Sanchez, Guardiola was previously reported to have been promised funds in the summer to land a top forward with Atletico Madrid's Antoine Griezmann touted as a target.
However, the Mirror states that Hazard is the new priority now with the 27-year-old's current contract stand-off with Chelsea likely to give the Sky Blues a boost.
Hazard's contract expires in the summer of 2020 and so far, he has stalled on extending his deal with Real Madrid having a long-standing interest in the former Lille man.
It is believed that the contract situation will lead to Hazard becoming available on the market this summer with City ready to challenge Madrid for his signature and break the British transfer record in the process.
If the current Premier League leaders do sign the Belgian, it is reported that he will be offered the same terms that saw his compatriot Kevin de Bruyne sign a new £300,000-a-week contract ($425,100-a-week) at City, with another possible £50,000-a-week ($70,850-a-week) in add-ons.
City are also confident that the lure of Guardiola and Madrid's current crisis will be enough to land their man. Madrid boss Zinedine Zidane, Hazard's boyhood idol, is currently under a lot of scrutinies with the club currently in fourth place in La Liga.
And with top earners in Cristiano Ronaldo and Gareth Bale needing to be moved on before the arrival of another star, a scenario that will see Hazard move to Spain is complex at the moment.