The Schindler's List star was left devastated when Richardson passed away in 2009 after suffering a brain injury in a skiing accident in Montreal, Canada.
Neeson sparked rumours he had started a new romance when he was spotted holding hands with British businesswoman Freya St Johnston last month (Sep10).
But new reports have emerged suggesting he has begun dating Leslie Slater, who he met on a flight to Paris, France six weeks ago.
The pair was spotted sharing an intimate meal at a New York restaurant, before Slater spent several hours at Neeson's apartment.
An onlooker tells Britain's The Sun, "When his date arrived they gave each other a big hug and kiss. Then for the next couple of hours they barely touched their food as they laughed and stared into each other's eyes."
Another source tells the publication, "Leslie's been going on about Liam for weeks and he texts her all the time. They get on really well and, due to her work, she travels extensively and can get about easily. She agreed to see him in New York and they went out together a few times. Liam seems to really like her."