The duo fell apart after 38-year-old former Spice Girl failed to get in touch with Cole when her husband Ashley cheated on her, reported Daily Star.
In retaliation, Cole, 29, has referred to Beckham's fashion range as designed for "older women" in the past.
"Posh has offered Cheryl an olive branch since moving back to London. She emailed inviting her and boyfriend Tre to dinner and Cheryl accepted," a source said.
"A lot of time has passed since they fell out and they both want to move on," the source added.