The boyband star, 20, and 32-year-old Foster visited a pumpkin patch in Los Angeles together on Wednesday (08Oct14) to pick out their Halloween props.
The rumoured new couple avoided showing any public displays of affection, but the stars appeared close as they perused the pumpkins on offer.
Styles and Foster have yet to comment on the romance reports.
The singer is no stranger to dating older women - he previously hit headlines in 2011 when the then-17 year old embarked on a relationship with British Tv presenter Caroline Flack, who is 14 years his senior. They split in January, 2012 and Styles went on to date Taylor Swift.
Foster was last linked to Lindsay Lohan's ex Samantha Ronson, but they parted ways in 2012 after nine months together.