Saunders is set to announce his next title defence later today but it is widely expected to be against Monroe, known as the Mongoose.
Saunders had been due to face Avtandil Khurtsidze earlier this month but the Georgian was forced to withdraw after being arrested in New York.
But now the 27-year-old is due to defend his WBO middleweight title for the second time on September 16 and he is keen to get the war of words started early.
“The Mongoose – I’m going to show you what I’m going to do,” Saunders said, raising his middle finger to the camera.
Billy Joe Saunders is likely to face Willie Monroe in his next fight
“And still. WBO king. Billie Joe Saunders.”
Saunders is one of just two champions in the middleweight division – Gennady Golovkin holds the IBF, WBA and WBC belts.
Eubank Jr is also billed as a world champion by his promotional company but he holds the IBO middleweight belt, which is not widely recognised as a major world championship.
Billy Joe Saunders is 24-0 in the ring
And Saunders is also unimpressed by the 26-fight boxer’s 25-1 record, criticising his defensive technique despite a win last weekend over Arthur Abraham.
“Eubank is nothing but a p***y,” Saunders added.
“I will beat you with my eyes shut. I will beat you with these sunglasses on.
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10 of the most shocking moments in boxing history Sat, May 2, 2015
From the time Tyson bit Holyfield's ear, to 'The Thrilla in Manila,' we take a look at the most shocking moments in the history of boxing.
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Mike Tyson bites Evander Holyfield on the left ear in the third round of their WBA Heavyweight match at the MGM Grand in Las Vegas in 1997
“Every time someone goes forward with a double jab and you go [hides behind palm].
“What’s all that about, you little p***y?
“I signed to fight you twice. W****r. I’m No1.“