Having already won the Group Three Princess Margaret Stakes, she travelled to York last week and won her third straight race on the trot - the Group Two Lowther Stakes.
Connections are now aiming for a further step up in class in Newmarket's Cheveley Park next month.
"We'll give her one or two days to be happy and then we'll start riding her again," said trainer Ismail Mohammed.
"She is a classic already, she's shown us in every race that she's improved.
"Next month it is our plan to go to Newmarket for the Group One, the Cheveley Park."
Zain Claudette's success at York was jockey Ray Dawson's biggest winner to date, with the Princess Margaret having been his first Group success.
"We like to help the young guy get some kind of Group race," added the Newmarket trainer.
"He's been there from the Listed race to the Group Three and he is doing really well."
Dawson spoke with confidence post-race about Zain Claudette's Group One potential, and also indicated a trip beyond six furlongs will eventually prove within her compass - with the 1000 Guineas discussed for her three-year-old season.
Mohammed added: "We will be targeting the Guineas for next season.
"She handles everything very well and she can definitely go further. She (also) has a very good turn of foot."
Owner Saeed Al Tayer has been the recipient of multiple offers for the filly, but she will be staying at her trainer's Grange House Stables.
"She has run so well for us and she is improving - we don't want her to go and we have had a lot of offers," said Mohammed.
"We have to keep her. She is giving us so much fun and happiness - for a small yard, to get any Group race is so good for us."