After victory over West Ham on Saturday, Saka revealed Henry was in regular contact.
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The England winger scored from the spot in the 2-0 win - on his 200th appearance for the club.
"Thierry messaged me this morning to remind we lost the last two games to West Ham at home," Saka said.
"He is always pushing me. I am really happy to have my name with his records."
The 24 year-old also said: "It showed the progress we have made. The last two seasons we slipped up at home against West Ham and we wanted to put that right today."