Van Gaal was Guardiola's manager during their time together at Barcelona and made the former midfielder his captain at Camp Nou.
The Spaniard has since followed his old boss into management and enjoyed great success during his time in charge of both Barca and Bayern Munich.
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His next challenge will see him replace Manuel Pellegrini at the Etihad Stadium next summer, where he will immediately become a rival of Van Gaal, though the Dutchman says he will be happy to see him.
He said: "He is my former captain so I am very pleased to see him. And I can speak Spanish so it is very convenient for me!"
Van Gaal was talking after United's 3-0 win over Stoke City on Tuesday night, which came courtesy of goals from Jesse Lingard, Anthony Martial and Wayne Rooney.