The duo both started against Crystal Palace on Saturday, and Zarate scored a fine opening goal in the 3-1 victory at Selhurst Park.
The Argentinian forward had a fine campaign for Velez Sarsfield in his homeland last season after a turbulent four years with Lazio, and Allardyce thinks the 27-year-old is beginning to fully realise his potential.
"The lad has grown up and matured,” said Allardyce.
“I remember his loan spell at Birmingham six years or so ago. He's been to Italy and back to Argentina since then, and scored some goals.
“I think he looks, at his age, a mature player with a lot of quality in the final third, which is something different from what we have."
The 24-year-old Kouyate has also impressed his new manager.
"I think he's got the modern-day midfield player written all over him," said Allardyce.
"The one thing maybe he might be missing is a goal or two, I don't know yet, but certainly he gets in that area a few times.
"He's high-energy, two-footed, great box-to-box, committed in the air, and he tackles.
“I think it's great to see a player that comes in with a big smile on his face every day. He's living his dream by playing in the Premier League."