Andre Ward beat Sergey Kovalev in a massive unification fight last year
Eubank Jr's father and trainer Chris Sr, himself a former two-weight world champion, declared earlier this week that his son would "wreck" Ward in the ring.
But as WBA, IBF and WBO light-heavyweight champion, Ward thinks both Eubanks have got a little ahead of themselves.
"You can’t come out the crib running," Ward told Boxing News.
Chris Eubank Jr will face Renold Quinlan on Saturday night at Olympia
"You’ve got to crawl before you run and him being a former fighter and a former champion, [Chris Sr] knows that, he knows that all too well.
"I’ve seen a lot of overly zealous fathers get their sons knocked out and get them in bad situations throughout the course of my career.
"The zealousness is cool, make sure it’s not too much, too soon.”
Eubank Jr has one defeat on his 24-fight record, losing to Billy Joe Saunders at the ExCeL back in 2014.
But now he will fight Renold Quinlan for the little-known IBO super-middleweight belt at the top of the first ever card on ITV Box Office this Saturday.
And Ward believes the pair are not doing more than trying to ensure the event gets its due publicity.
“I understand how the game works," Ward added.
"This is the first time they’ve ever brought my name up, the week of this fight.
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"They’re trying to drum up this fight, get the people excited.
Chris Eubank Jr is an exciting fighter with just one defeat on his record
"They’re calling out some big names, they’re trying to sell some more pay-per-views, get some more people on the seats.
"When I was younger, that stuff used to rile me up and I’d want to respond.
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"You want to prove yourself and any time anybody says anything, it can strike a nerve.
"I’ve been in the game so long I just laugh at the kind of stuff.”