However, with Chelsea failing to qualify for the Champions League, Hazard is unlikely to commit to a new contract at Stamford Bridge, with his current terms expiring in 2020.
Guardiola earlier said according to the Sun that he would not splash the cash during the window, unless a suitable superstar became available. He has already told the board how much he admires him. They know his value will drop if his deal continues to run down.
The winger, who is valued at £90million by Transfermarkt, has been a key player for Chelsea since he arrived from Lille and will be disappointed with the way the campaign has gone.
Guardiola is planning to use the influence of Belgian team-mates Kevin De Bruyne and Vincent Kompany to lure the Chelsea attacker.
The Algerian is still on his shortlist along with Crystal Palace's Wilfried Zaha and Leon Bailey, but Hazard would be his top priority.
Hazard, who has won the Premier League twice at Chelsea, fits the bill and has suggested he could leave if the Blues do not make the right signings in the summer.
He scored 36 goals in 147 matches in his five year reign at the club.
Pep Guardiola confirmed this week that City would only look to sign "one or two" players during the summer transfer window and said the club were not in a position to spend "another £300m" on signings.
They also failed to win the Champions League and League Cup, leaving tomorrow's FA Cup final against Manchester United as their last chance of silverware this season.
Eden Hazard fully expects to be at Chelsea next season but says he is in no hurry to sign a new contract as he wants the club to prove their ambition by bringing in players capable of winning the Premier League.
The Belgium worldwide has been attracting unwanted interest from Real Madrid and the Blues are determined to keep him at Stamford Bridge.
Evidence of Planet Nine Possibly Found
So, in order to reach their unexpected conclusion, the team used some computer simulation of the solar system. However, the mere presence of this object and it odd orbit might make this a very clear possibility.