The Red Devils saw their opening bid of £52.4m ($66.8m) for the Spain international rejected by the European champions. According to Sky Sports, Real are looking at a fee of £78m ($99.5m) to part ways with their striker and it does not include De Gea as a part of the deal.
United goalkeeper has been heavily linked with a move back to the Spanish capital. However, it is believed that Real manager Zinedine Zidane wants to continue with Keylor Navas as the club's first choice keeper next season. This has forced the La Liga winners to abandon their pursuit of signing De Gea.
Morata still remains a target for United manager Jose Mourinho, who wants to strengthen his side's attack for the next season. The 20-time English champions will continue the negotiations with Real and are confident of landing the attacker.
The 24-year-old was the second choice striker for Zidane last season as Morata was behind Karim Benzema in the pecking order. The former Juventus man made only 14 starts in the league, which is nine less than the French international.
Despite spending more time on the bench, Morata has scored 20 goals for Real in all competitions. His agent Juanma Lopez has already made it clear that his client will not spend time on the bench in the 2017/18 season and the player will take a "clear and definitive" decision over his future will be taken in the "coming days."
Meanwhile, the Guardian reports United believe they can convince Real president Florentino Perez to lower the asking fee from £78m to £60m ($76.5m) for Morata. The striker, who scored in Spain's 2-2 friendly draw against Colombia is Mourinho's primary attacking target in the transfer window.