An insider also said: "They even shared a kiss on the gym floor and were super playful with each other between sets."
It comes after sharp-eyed fans first noticed Affleck's watch as he smoked a cigarette on the balcony after reuniting with Lopez at her home on the weekend.
It appears to be the same watch that he wore during his cameo appearance on Lopez's 2002 music video for her song Jenny from the Block.
Just a month ago, Lopez confirmed that her relationship with former New York Yankees player Alex Rodriguez had come to an end after dating for four years and being engaged for two.
And a source told People last week that Lopez had returned to Los Angeles to spend more time with Affleck as they reunited earlier in the week.
"Jennifer was just in Los Angeles for a couple of days. She spent time with Ben. They have kept in touch every day since their Montana trip."
The source went on to explain that the couple are navigating a long-distance relationship together.
"It's a tricky situation since they live so far from each other, but they both seem committed to making things work."