The Dutchman is currently managing Egyptian side Al Ahly, who completed the sale of Ramadan to Stoke for €6 million (£5m) on Monday.
The 19-year-old has been hailed as one of the most exciting young players in African football and Jol believes the winger has the potential to move on to Manchester United.
“I sent a message to Jose Mourinho, who is in touch with me, asking him to keep an eye on Ramadan with Stoke City as he is a brilliant player and he can play at Manchester United after that,” said Jol.
“I tried to keep Sobhi in the team's squad but he insists on the English Premier League chance.
”I hope he will succeed in England and I will always support him there.”