The Beatles legend, whose four-year marriage to Heather Mills officially ended last month, has been on holiday with US heiress Nancy Shevell but is also said to be romancing actress Rosanna Arquette and former Olympic horse rider Tanya Larrigan.
A source said: "Paul is keeping his options open and is seeing three women."
"He is free to play the field now and has no plans to commit to another serious relationship. He just wants to go out and have fun."
Despite his romantic Caribbean break with Nancy, Paul has remained in contact with Rosanna, 48, and the pair have met several times in London for intimate dinners.
Paul, 65, has also grown close to 53-year-old Tanya - who is the daughter of one of Paul's friends from his Beatles days - after she supported him through his bitter divorce battle with Heather.
Meanwhile, Paul has paid a moving tribute to his first wife Linda, nearly 10 years after she died of breast cancer.
Paul said: "She was a great person to hang out with. She was beautiful, smart and talented. She was a very natural girl, naturally blonde, so funny."
"She didn't know she was dying - she was such a strong, forward-thinking lady. She was fighting right up to the end."
