Fodé Touré Ballo, 18, is still on amateur forms at PSG and has been tabled a contract offer by the Hammers, says Foot Mercato.
Ballo is a left-sided midfielder and a France youth international. He has played 12 games for PSG reserves this season.
West Ham now hope to bring the youngster to London in the summer.
The Hammers also have Robert Lipovac from BK Hacken trialling with their U21 squad this week.