The Blues were 3-0 winners against defending Premier League champions Leicester City on Saturday evening after goals from Diego Costa, Hazard and Victor Moses.
The former Lille winger has now scored three times in eight Premier League appearances under Conte in the 2016-17 campaign so far.
Hazard endured a miserable run of form under Jose Mourinho and Guus Hiddink last term after the Belgian forward failed to find the back of the net until April despite being named the 2015 PFA player of the year a mere 12 months earlier.
Former Liverpool captain Souness explained why it is paramount that Conte keeps Hazard happy if the Chelsea manager is to enjoy a successful first season at Stamford Bridge.
“It is paramount that you get Eden Hazard playing where he is happiest,” Souness told Sky Sports on Saturday afternoon.
“He would be appear to be happy in that position [behind Diego Costa]. You’ve got to have all the players settled and happy.
“You’ve got to get your best player where he feel he plays best.”
Chelsea are in fifth place in the Premier League table and three points behind leaders Manchester City ahead of the visit of Manchester United at Stamford Bridge next weekend.
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