The 'Boys And Girls' singer met 22-year-old Cheshire through friends and hit it off at a Select Models catwalk show, according to The Sun.
The pair, who were photographed together outside London's Mahiki nightclub on Friday, have apparently been dating for a few weeks and have enjoyed "a fantastic time together during the summer".
The source added: "Pixie and Oliver are dating. Pixie hasn't declared it publicly as she doesn't want to seem too keen or jinx it.
"It is early days but they both really like each other. They get on brilliantly and are having fun together."
Another source said: "They are getting more and more touchy-feely when they're out. They've tried hiding it but like each other too much."
Cheshire's Facebook page currently lists the model as 'in a relationship'.
Lott has previously been linked to several male music stars including Professor Green, Joe Jonas and McFly's Danny Jones.