City announced the £52 million signing of the Monaco left-back on Monday, with former team-mate Mbappe - also a top target for Pep Guardiola's side, wishing him luck on his new adventure.
Mbappe said on Twitter: "Good luck to you buddy, I'll miss you very soon."
Mendy replied: "I'll miss you a little bit too, my friend. You already know that."
mon sang toi aussi vite fait tu c'est déjà— Benjamin Mendy (@benmendy23) July 24, 2017
Mbappe has been linked with a world-record transfer to the European elite since the end of last season following a sensational breakthrough campaign.
The 18-year-old struck 26 goals in all competitions for Monaco, leading the club to the Ligue 1 title, a Coupe de la Ligue final, and a Champions League semi-final following a two-legged victory over Manchester City.
Mbappe's six Champions League goals in six starts, including one in each of the meetings with Pep Guardiola's side, saw the France striker emerge as one of the most sought after forwards in world football.
MBAPPE TO MANCHESTER CITY
Goal revealed that City have stepped up their interest in striking a deal for Mbappe as a result of Paris Saint-Germain's rival interest in Arsenal's Alexis Sanchez.
City chiefs were confident of landing the Chile international before PSG entered proceedings and spoke to the forward and his representatives in Paris last week.
Now, determined to add an attacker to the squad before the 2017-18 campaign, Guardiola and his team have turned towards Mbappe, though understand the difficulties behind any potential deal.