From Been There, Done That book by Eddie Fisher :

Some of the things she revealed did surprise me, though, like her affair with Sinatra. She told me that she'd had an affair with Frank Sinatra while she was married to Wilding—and had gotten pregnant with Sinatra's child. According to Elizabeth, she wanted to divorce Wilding and marry Sinatra, so she called him and asked him to marry her, but he didn't want any part of that. And then she told me that Frank's manager put her in a limousine and drove her to Mexico—she described it as some dirty place in Mexico—where she had an abortion.

She always spoke about Sinatra with contempt, and I was positive she would never forgive him. She made it clear that she hated him. She was always cursing him, always criticizing him, always bringing up that abortion.

Then she won her Oscar for her performance in Butterfield 8. After the ceremony she was holding court in our bungalow at the Beverly Hills Hotel. Everybody in Hollywood came there to congratulate her, all the actors and directors and writers, and she allowed them in one at a time. Finally Sinatra showed up. I was all ready for a big scene; I thought this was going to be one of those great moments of payback.

Instead she welcomed him and spent more time with him than with people she genuinely liked, people like John Wayne. Elizabeth was an incredibly complicated woman, but I've never known anyone who was more honest about her feelings. Painfully honest, believe me. This was the one time, though, when she was truly a hypocrite.

Several years later, when Elizabeth and I were involved in a court fight, my good buddy Sinatra called and said, "Why don't you lay off Liz?"

I laughed at that. "Oh, come on, Frank," I said. "You know Elizabeth almost as well as I do." He knew exactly what I meant by that and backed off. End of conversation

From His Way by Kitty Kelly :

He swore to Mona Freeman that he didn’t care if he ever saw Ava again, and he said the same to Judy Garland, whom he dropped abruptly when she wanted to become the next Mrs. Sinatra. Elizabeth Taylor got the same treatment toward the end of her unhappy marriage to Michael Wilding when she found herself pregnant by Frank and wanted to marry him. He arranged an abortion for her instead.