The Mexican-American actress and former model was being interviewed on the El Show del Mandril on Radio Centro 93.9 when she said she firmly believed that Mr Trump gave a story to the Enquirer after she told him she wouldn’t go out with him.
Ms Hayek, 50, said: “When I met that man, I had a boyfriend and he tried to become his friend to get my telephone number. He got my number and would call to invite me out.”
However, when he did call, Ms Hayek refused the Republican candidate’s advances.
She went on to strongly hint that Mr Trump then decided to take his revenge by contacting the National Enquirer, which is renowned for printing far from salubrious stories about celebrities.
Ms Hayek said: “Someone told the National Enquirer. I’m not going to say who because you know that whatever he wants to come out, comes out in the National Enquirer. It said that he wouldn’t go out with me, because I was too short.”
After the story was published, Ms Hayek said Mr Trump called her and left a message on her answer machine, saying: “Can you believe this? Who would say this. I don’t want people to think this about you.”
She said Mr Trump then thought she would go out with him because she would not want people to think that he had refused a date with her.
Ms Hayek has long been a staunch supporter of Mr Trump’s rival Hillary Clinton, having taken part in a campaign broadcast on behalf of Mrs Clinton, in which she urged Latino voters to put their tick on their ballot paper in favour of the Democrat candidate.
She has also already criticised Mr Trump’s heavily controversial immigration policies.
Ms Hayek, who is married to French billionaire François-Henri Pinault, refuses even to speak Mr Trump’s name, saying she does not want to give him any more attention.
She added: “I’m aware that he would say anything to attract attention and create the publicity around him. If something generates publicity, I would never be surprised about anything he does.”