The FC Twente playmaker has been in fantastic form for the Dutch club.
The report claims that Celtic and co were watching him in action as Twente beat Heracles 4-0 earlier this season and are now said to be continuing to monitor his progress as Ziyech finds his best form in the Dutch top flight.
All three teams should certainly be keeping tabs on the player.
Ziyech has been linked with a heap of top clubs over the years after shining at Twente since his move from Heerenveen.
The attacking midfielder has been sublime for Twente for the past two seasons, scoring 26 goals in 57 appearances from midfield - so there is little wonder top clubs in Europe are keen.
Celtic, Leicester and Swansea will therefore seem like underdogs. But Twente are in financial ruin so he would not be as expensive as he is worth.
Meanwhile Celtic remain a big club and Ziyech may see them as a stepping stone toward the Premier League whilst still potentially playing in Europe.
Leicester are looking like potential Premier League winners and are also on course to be in the Champions League next season - so that would help their cause.
Swansea on the other hand have attracted some decent talent to the club in recent times and Ziyech would follow in that pattern.
The Dutch-born Moroccan international looks like an exceptional talent and if Celtic, Leicester or Swansea brought him in this summer it would be a massive coup.