By TMZ Sports

WBC/WBO/WBA welterweight champion Floyd Mayweather Jr. is allegedly waging a telephone war on Andre Berto -- making harassing and annoying calls to the boxer ... and it's all over a woman, this according to Berto.

Berto appeared on "TMZ Hollywood Sports" on Wednesday and told us that he respects Floyd as a fighter -- but he's sick of all the drama that's been going on outside the ring.

FYI -- Mayweather recently said he's considering Berto as his next opponent for September 12th at the MGM Grand.

"If we gonna fight, we gonna fight. If not, take my name out your mouth brotha," Berto said. "For damn sure it would be a good fight. I'm one of the only guys who can match him speed for speed and everyone knows me for having explosive power. It's going to be a lot better than that Pacquiao sh*t that you had."

But Berto says he's more frustrated with the wave of harassing phone calls he's received lately ... and he's convinced Mayweather is the one behind the telephonic hostility.

"I know it's him on the other line. I can hear him breathing on the other end of the phone. Stop getting people to call my phone, bro, and asking me about this person and that person. Don't do that sh*t. That sh*t is lame. It's corny. He has too much money for that."

So, why would Floyd do it? Berto suggested Floyd is upset with him over an issue involving a woman.

Sources connected to the situation tell us ... Mayweather is upset that Berto is friendly with his ex-fiancee Shantel Jackson and her new boyfriend Nelly.