Williams announced on Wednesday she is expecting her first child with fiance Alexis Ohanian, who is white.
Nastase wasn't asked about Williams, but still, he deliberately made the comment and was clearly audible.
The International Tennis Federation released the following statement regarding Nastase's remarks, noting that an immediate investigation has been launched.
With Konta leading Romania's Sorana Cirstea 6-2, 1-2 in the second rubber in Constanta, Nastase became embroiled in a row apparently about noise from the crowd. "Chocolate with milk?" Nastase said - though the Hall of Famer claims he doesn't believe what he said was racist, and touted having a good relationship with Williams.
And as he left the 70-year-old was then alleged to have called Johanna Konta and Anne Keothavong "f***ing bitches", which left the British number one in tears and the match suspended while she went to compose herself.
He was sent off the court by referee Andreas Egli and, after initially taking a seat in the stands, was then escorted back to the locker room.
A day later Romania received a warning for unsportsmanlike conduct from umpire Jaume Campistol in game three of the second set with Konta appearing to complain about something that had been said in the crowd.
"Nasty" Nastase was tossed from Saturday's World Group II playoff against Britain for his "serious misconduct" after verbally abusing members of the United Kingdom team.
"I figured he would probably be unhappy with what we'd written, even though he didn't dispute that we reported accurately what he had said".
Shriver says that although she spoke to friends about the two-time Grand Slam winner's behaviour during the pair's playing days, she did not officially report it. "You're stupid, you're stupid". The English player just stormed off without even asking permission to leave the court, and I admit that's when I called her a b--. "I felt the crowd today were a lot fairer and I felt they supported Simona well". I never cried and left the court, I stay there and I play.
"What Nastase said to me and Johanna is language that is not appropriate for anyone to speak to any other human", she told fedcup.com. "You're stupid, you're stupid".
"I've played all over this world, they called me from gypsy to b-- to a-hole to idiot", said Cirstea.
The 23-time major champion wrote on Instagram on Monday: "It disappoints me to know we live in a society where people like Ilie Nastase can make such racist comments towards myself and (my) unborn child".
Halep, the world No 5, who had asked for Nastase to be made captain, later seemed to play down the offending comments, saying: "He's joking all the time, and I'm 100% that that was a joke".