Depay joined Premier League giants United from Dutch side PSV Eindhoven in the summer of 2015.
The Netherlands international forward arrived at Old Trafford with a strong reputation, but the youngster has failed to make a huge impact so far.
Elia, who had a loan spell at Southampton from Werder Bremen in 2015, has revealed that he advised Depay against moving to United.
“I thought Memphis first had to make a stop, first choose a club like Tottenham Hotspur,” The Metro quotes the 29-year-old winger as saying.
“United are so big, the pressure is so high. He had to immediately make an impact at such a club, while everyone would watch him.
“Memphis accepted my opinion, but said, ‘I’ll try to give my all and I’m confident that I can succeed there’.”
United are one of the biggest clubs in the world and the biggest in England, and as Elia suggests, scrutiny of players at Old Trafford is huge.
Tottenham themselves are a big club, but perhaps joining the North London outfit would have allowed Depay some time to get used to the Premier League.
However, the Dutch youngster would have had to still compete for his place at Spurs and still show his quality.