In Shulchan Aruch O"C 14:1 it says:

ציצית שעשאן אינו יהודי פסול, דכתיב: "דבר אל בני ישראל", לאפוקי אינו יהודי

 

Tzitzis that a non-Jew made are invalid, for it says, "Speak to the Children of Israel (Num. 15:38)" to exclude a non-Jew.

And the Mishnah Berurah there:

...שעשאן — פי' שהטילן בבגד פסול אפילו בישראל עומד על גבו ומלמדהו לעשות לשמה

 

that made - meaning: that tied them to the clothes - are invalid, even if a Jew stands over him and teaches him to do it for the sake [of the commandment]...

So it is permitted for a non-Jew to make the cloth, but attaching the strings would render it invalid.

In Shulchan Aruch O"C 14:1 it says:

ציצית שעשאן אינו יהודי פסול, דכתיב: "דבר אל בני ישראל", לאפוקי אינו יהודי

Tzitzis that a non-Jew made are invalid, for it says, "Speak to the Children of Israel (Num. 15:38)" to exclude a non-Jew.

And the Mishnah Berurah there:

...שעשאן — פי' שהטילן בבגד פסול אפילו בישראל עומד על גבו ומלמדהו לעשות לשמה

that made - meaning: that tied them to the clothes - are invalid, even if a Jew stands over him and teaches him to do it for the sake [of the commandment]...

So it is permitted for a non-Jew to make the cloth, but attaching the strings would render it invalid.