But Eboue has warned even the best young players can struggle to deliver on their potential, like teenage sensations Jack Wilshere, Alex Oxlade-Chamberlain and Theo Walcott during his time with the Gunners.
Versatile forward Mathis, 16, signed as a scholar with the Blues after joining from Watford last year.
And his dad reckons Chelsea’s commitment to fielding young players gives his boy a good chance of making his mark at Stamford Bridge.
Eboue senior said: “I’m very, very proud of Mathis, and very happy for him.
“It doesn’t matter, for me, that he’s doing this in a Chelsea shirt, and I’m an ex-Arsenal player.
“When he was younger he was playing for Watford and doing really well there, and then one day he told me that Chelsea wanted to sign him.
“I said it was completely up to him what he wanted to do, and I’m just really happy with how things are going for him.
“For me, at 16, nearly 17, I think I would want to stay at the club, because you can see how much they like to use their younger players.
“So for him, I think it’s better to stay at Chelsea, because when he turns 17 very soon, they’re going to look to use him – maybe next season.”
But Eboue saw young Gunners Wilshere, Oxlade-Chamberlain and Walcott all struggle to live up to the hype after their early taste of fame.
The right back spent seven years at Arsenal after joining them in 2004, immediately after Arsene Wenger’s Invincibles won what remains the club’s last Premier League title.
Eboue toldLadbrokes at the launch of Ladisfaction:“You know, they were all very good players, but if we were going to win the Premier League, we needed players who were going to be ready.
“Of course, Jack was very good, but people were putting so much expectation on him, but it’s not easy.
“You know, as good a player as he was, we never won the league, or anything like that, so he didn’t quite live up to what everyone had said he was going to do.
“For me, your dream as a young player at Arsenal should be to win a trophy for the club. But if you are not focused, or giving your best every single time, that’s not going to happen.
“I really liked playing with all three of those guys, but you look back at what they achieved during their time with the club, and we didn’t win anything.
“With Theo Walcott, I don’t even know if he’s stopped playing football now or not…
“The young English players have to stay focused on the game and their goals.”
Mathis has had an encouraging start to his Chelsea career.
They’re going to look to use him – maybe next season.”
Emmanuel Eboue on son Mathis playing for Chelsea
He can play off both flanks and as an attacking midfielder, and has scored three goals and provided one assist in nine appearances for Chelsea’s Premier League Under-18 team.
He has also made two substitute appearances in the Uefa Youth League.
Young Eboue, who was born in Watford, is an England youth international.
But he could yet opt to play for Belgium, his mother’s homeland, or follow in his dad’s footsteps with the Ivory Coast.
Eboue senior said: “I watch him as much as I can.
“I want him to be the best, of course. But to be better than me? I don’t know!
“I can remember a couple of years ago when he was playing for the national team – the under-15s [England] played against the Ivory Coast, and afterwards the president of the Federation called me to tell me he’d seen my son, and thought he was very, very good.
“I was so happy to hear that, and the good thing he’s got is that he’s still able to play for England, Ivory Coast and Belgium, so he has a lot of options there later on in his career.”