Andrea Brown reportedly fell out with the star in 2007 over her relationship with her husband, film producer Stephen Belafonte.
Brown, who lives in Los Angeles with her family - including her three daughters - has not spoken to her mother since she wed Belafonte that same year (07).
Andrea shared photographs via Twitter.com on Friday (29May15), her eldest daughter's birthday, and expressed her desire to be reunited with the star, who she misses "forever".
Melanie's younger sister Danielle, who is also believed to have a difficult relationship with Brown, has joined her mother in trying to reconnect with the star.
Andrea tweeted a photograph of Brown doing the splits as a teenager, and wrote, "40 today hope ur birthday is as special as u r 2 me luv and miss u FOREVER X. (sic)"
She then posted a picture of herself applying make-up to a young Brown, and added, "Today I have a 40 (year) old child loved and missed so badly!! Official 1st makeup artist ME!! (sic)"
Danielle also tweeted her sister, adding, "Happy 40th Birthday to my one and only big sis @OfficialMelB (sic)."