Hazard continued his fine form for the Blues with his delightful flick opening up space for Willian to find Tiemoue Bakayoko who scored Chelsea's opening goal on Tuesday (12 December).
Willian and Pedro later found the back of the net as well as Cole labelled them "world class" players. However, he feels Chelsea should build their side around the "special" Hazard, having played alongside him at Lille.
"When you have a gem like Hazard in your side, you have to build your team around him," Cole told BT Sport.
"Pedro and Willian are world-class players but Hazard is special."
With eight goals and three assists in his last 13 games in all competitions, perennial interest in Hazard from Real Madrid will only continue to grow.
The Belgian has flirted with the idea of a move to Spain in the past and is reportedly stalling on a new deal to take his Chelsea contract beyond 2020 as he fears it would end his chances of a move to Madrid.
However, the 26-year-old recently put those rumours to rest, for now, stating that he is happy at Stamford Bridge and that he will see what happens at the end of the season.
Meanwhile, he also spoke about the effects of his side's added fixture congestion this season due to the Champions League following the Huddersfield win.
After not having any European football last season, which many believe proved pivotal to Chelsea's league-winning campaign, Hazard claims it has been draining this year, with the reigning champions currently lagging 14 points behind table-topping Manchester City.
"Yes of course [it is draining]," Hazard explained. "We have a lot of games in a short period. We didn't have this last year because of no Champions League.
"But since I came to Chelsea for six years now, every year is the same. We can deal with that. We have a lot of players in the squad."