Born and raised in Paris to an Algerian family, Isack Hadjar has impressed Red Bull bosses after finishing runner-up in the Formula 2 championship this year.
Veteran drivers Fernando Alonso and Daniel Ricciardo both denied on Thursday that they were about to leave their teams to join Red Bull next season.
New Zealander Lawson has driven the last three races for AlphaTauri as a replacement for Ricciardo, who broke his hand in practice last month.
Daniel Ricciardo described his misfortune on only his third race back from a sabbatical as "really unfortunate and frustrating".
The longest season in Formula 1 history starts this weekend with the Bahrain Grand Prix
Bahrain Grand Prix: AlphaTauri driver Pierre Gasly's car suddenly caught fire during the 46th lap of the Bahrain Grand Prix, which resulted in the Safety Car being brought out.
Japanese youngster Yuki Tsunoda and Frenchman Pierre Gasly will stay at AlphaTauri for the 2022 Formula One season, the team announced on Tuesday.