However, a representative for the baseball star has insisted that there is nothing happening.
They said: "There is absolutely zero there. They've been friends for 15 years."
It comes after a source revealed that Affleck and Lopez are "inseparable" at
the moment.
An insider said: "They are inseparable and it's going really well, Jennifer has never been happier and knows it was meant to be ... Her kids really like Ben and think he's funny and fun to be around. He's totally won the family over with his charm.
"Ben was very good with them. He was asking them questions and smiling. He was very engaged and seemed to like hanging out with them."
The family all went out together for a dinner out and Lopez's mother Guadalupe has continued to develop a good relationship with Affleck and is "thrilled that they are back together now".
A source said: "In the past, Jennifer's mom and Ben were very close. Guadalupe loved Ben. She was sad when they couldn't work things out years ago. She is thrilled that they are back together now."