The stars, who are rumoured to be getting back together, want relatives to give their blessing for the couple's reunion, The Sun reports.
A friend said: "Cheryl and Ashley are a sealed deal - but they need this dinner to clear the air between the families. There's still bad feeling, particularly on Cheryl's side."
Cheryl's mum Joan and brother Garry will join Ashley's mother Sue and brother Matthew at the meal, which is due to take place in Essex.
Meanwhile, former X Factor judge Cheryl is said to have bought footballer Ashley a pendant symbolising "love, strength, togetherness and eternity".
In return, he has bought her a seven foot air ice hockey table for their old marital home in Surrey and she has secretly moved her belongings back into the house.
Ashley was recently accused of sleeping with several women while trying to win Cheryl back, including a Virgin Atlantic air hostess who said he "acted like a single man".
Watch Cheryl Cole's video for 'Parachute' below: