His efforts have been drawing admiring glances from afar for some time, with talk of a future switch to Spain refusing to go away.
Chelsea have fought hard to fend off the rumours and Lampard believes there will remain little substance to them for as long as Hazard remains happy and consistent in his current surroundings.
The Blues legend told BT Sport: “If you are Eden Hazard or any top player in the world, the talk of Real Madrid and Barcelona will always hang over you whether it’s spoken about out loud in the newspaper or whether it is just a fact they go after the best players in the world.
“Eden Hazard is one of those so I don’t think it’s going to be any problem.
“He’s very aware that probably for the last two or three seasons that these big teams would like to take him from Chelsea.
“He doesn’t change anything as long as he performs week in week out.
“And he certainly has in recent weeks, then nothing changes as far as I’m concerned.”
Hazard recently passed up the opportunity to curb the Real reports when pressed on the ongoing interest in his services.
He did admit to being settled at Stamford Bridge, but also talked up his “admiration” for the current La Liga and Champions League title holders.
Hazard told Canal+: "I am always very fine at this club. I still have two years of contract [left]. When I feel the desire to leave, I'll leave. But, for now, I'm a Blue.
"We know the admiration that I have for Real, but I'm at Chelsea. Every year, things were said about me but I stayed.”
Hazard joined Chelsea from Lille in 2012 and has made 265 appearances for the club, helping them to two Premier League titles, a League Cup win, a Europa League success and himself to the 2014-15 PFA Player of the Year award.