Allen told Newsweek magazine that his relationship with Ms Previn began when he took her to a New York Knicks professional basketball game a little more than a year ago. Until then, he said, he 'never had any interest in her at all'.
The film director said that he and Ms Previn went to another game about a month later and 'gradually over a period of time a strictly talking relationship developed'.
'Only long after the relationship with Mia was finished did it very gradually drift into an intimate relationship,' the film director said. Asked if marriage is a possibility, Allen replied: 'Possible, uh-huh.'
Ms Previn told Newsweek about her relationship with Allen: 'I admit that it's offbeat, but let's not get hysterical. I'm not a retarded under-age flower who was raped, molested and spoiled by some evil stepfather - not by a long shot,' she said.
The former lovers are due to appear in court today for a hearing on the custody of their three children, two of whom are adopted. A meeting between Allen and Farrow arranged for Sunday was called off after Farrow refused to withdraw allegations that Allen had molested their adopted seven-year-old daughter, Dylan.
Authorities in Connecticut and New York are investigating allegations that Allen had sexually abused Dylan. He denies it.
Allen's dollars 5m ( pounds 2.5m) deal to make television commercials for an Italian supermarket chain will go forward, despite his personal problems, a spokesman for La Coop Nordemilia said yesterday.