The claims were made by model Alexandra Paressant, who said that Parker had slept with her in September, just two months after he and Longoria tied the knot in July this year.
However, both Eva and Parker are standing by each other and have denied there’s any truth to the rumors.
"I love my wife! She's the best thing in my life, and I have never been happier,” People mag quoted Parker, as saying.
Eva said: "Tony has been nothing short of the perfect husband."
Paressant said earlier that she met Parker for the first time at his wedding and sparks flew between them and eventually the two started exchanging saucy messages in September while Parker was in Paris at the Park Hyatt Hotel.
They then slept together, and continued seeing each other night after night in Paris until he left to San Antonio a short time later.
She further revealed that some of Parker’s sexual fantasies were not fulfilled by his wife Eva that led to the fling.
"We had room service. He said that Eva, sexually speaking, does not want to do certain things. She does not want to make love in front of a mirror, does not like [a] certain position and thinks that sperm gives acne," US weekly quoted Paressant, as saying.
Longoria's rep Liza Anderson had earlier called the allegations "completely, 100 percent false and untrue."
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