The Monaco striker is in high demand after an impressive season for the French champions last time out.
Spanish outlet Don Balon say Mbappe told Barca he wants a move to arch rivals Real though.
The 18-year-old is more convinced by Zinedine Zidane who has proven himself winning the Champions League in the last two seasons.
And the reports also say Mbappe thinks Real is a more secure project in which he could flourish.
He is unconvinced by Barca who face a period of uncertainty after Neymar completed his £200m move to Paris St-Germain last night.
The 10 favourites to replace Neymar at Barcelona
Mbappe was sensational for Monaco last season, netting 26 goals and providing 14 assists in all competitions.
But the striker isn’t the only name that has been linked with replacing Neymar at the Nou Camp.
Liverpool’s Philippe Coutinho, PSG star Angel di Maria and Chelsea ace Eden Hazard have all been touted as potential signings.
Barca will want to improve their squad significantly after losing out to Real in La Liga last season and being dumped out of the Champions League at the quarter-final stage by Juventus.
New manager Ernesto Valverde has added Nelson Semedo and Gerard Deulofeu to his squad so far this summer.