Indeed, Thompson believes both have similar styles of play and that the Brazilian possesses the potential to reach the Chelsea man's level.
The Reds icon admits it is a little early to call Coutinho 'the next Hazard' but feels his career trajectory is certainly heading that way.
Speaking over the weekend and before Liverpool's game with Bournemouth, he told Sky Sports: "Eden Hazard has a couple of years' experience ahead of Philippe but he's certainly displaying a lot of those qualities, the close control, the speed off the mark - he's electric.
"Coutinho glides past opponents very close to their bodies, like a slalom skier, and also has the ability to create chances like Hazard.
"It could be a little too early to categorise him as the next Eden Hazard but he's certainly heading that way and he could become as important to Liverpool as Eden Hazard is to Chelsea."
Ironically, Coutinho has begun his campaign better than Hazard, who has endured a quiet start to the Premier League season.
But the struggling Blues will no doubt bounce back, while the Belgian will also come up against easier challenges than a rampant Manchester City side and a high-quality Swansea City outfit.
The biggest issue for Coutinho at Liverpool, of course, is his consistency but, if he can overcome that hurdle, the 23-year-old may well become one of the world's best players. As Reds fans have seen with the likes of Luis Suarez and Raheem Sterling, however, maybe the Brazilian is better off remaining inconsistent - or a Barcelona or Manchester City might snap him up!