Southampton manager Ronald Koeman is thought to be keen on Townsend, but Spurs manager Mauricio Pochettino wants to hold on to the England international, according to The Express.
"Townsend is another player, he is in the squad," Pochettino is quoted as saying.
"He is an important player, he is a player for the English national team. He missed the World Cup with injury. We need to recover a player like him because he has great potential and very good quality."
Tottenham began their season with a 1-0 victory over West Ham United yesterday, while Southampton face Liverpool this afternoon.