Officers searched the grounds at around 4pm on Thursday (September 21).
An investigation of the area has taken place but no one has been found and there is no evidence of shots fired, police said.
One resident said they heard shots from the Norman House bus stop in Saxon Avenue around 3.30pm.
She said: "The police went past as the shots were happening. But a girl at the bus stop said there had been shots about five minutes before hand."
One witnesses reported seeing armed police officers in the area, which has not been confirmed by the police.
A Metropolitan Police spokesman said: "Police were called to Crane Park in Hounslow at approximately 4pm on Thursday, 21 September following reports of shots being fired.
"Officers attended and conducted a search of the area but no one was found.
"No evidence of shots fired.
"No arrests have been made."
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