Real Madrid are interested in signing the Belgian, who admitted it is his "dream" to join the Bernabeu club.
When Eden Hazard is on it, I do not believe there is a defender in world football who could live with him.
"Chelsea is one of the most exciting teams in the Premier League this year", he said.
Recent reports suggest that Chelsea have offered to make Hazard the highest-paid player in the club's history in a bid to persuade him to spurn an exit and remain at Stamford Bridge beyond 2020.
Kompany's Belgian global teammate has enjoyed a sensational start to the season under Maurizio Sarri, scoring seven goals and providing six assists in 14 Premier League games.
"But I want him here if he wants to stay here".
I know very well that there are discussions between the club and the manager of Eden every week, I think.
'Eventually a manager like this is what he needed, no matter where he was, to get the best out of him.
The Blues welcome table-toppers Manchester City on Saturday evening, and Keown feels it is the best game for Hazard to mark his return to form.
A loss to Wolves in midweek, 11 days after losing their unbeaten record to Tottenham, has heaped pressure on Sarri, whose idiosyncratic methods are now under question.
Madrid could also seek to include Mateo Kovacic in the deal.
Chelsea provisional squad: Kepa, Caballero, Rudiger, Alonso, Fabregas, Jorginho, Kante, Barkley, Hazard, Pedro, Kovacic, Giroud, Zappacosta, Willian, Cahill, Christensen, Azpilicueta, Morata, Luiz, Emerson Palmieri, Loftus-Cheek, Hudson-Odoi, Ampadu, Bulka.
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