The 18-year-old winger, who can also play as a left-back, was on trial with the West Brom U23 side, and also scored in the Baggies' 2-1 Premier League 2 win over Fulham last month.
However, it appears now that he will be returning to North London as Albion prefer their current academy stock over Robinson.
West Brom academy manager Mark Harrison said: "He [Robinson] trained well and acquitted himself well in the games.
"He worked really hard and showed a good attitude.
"But sometimes you need to look at your own players and who is ahead of them in the system."