Gremio's players believe it would be too soon for 18 year-old Douglas Costa if he was to make the move to Manchester United.
Gremio insiders say Costa can be as good as United star Anderson, but has a shy personality and will take longer to settle in Europe.
The club's captain, Tcheco, said: "He must be calm, his time will come. He has all the ability, but all the rumours are making him anxious.
"The time for Europe will come, for now, he should focus on getting into our first team."