The twins are highly rated in Lanarkshire and have made a few Scottish Championship appearances between them this season.
Celtic are keen to sign the 17-year-old duo, reports The Scottish Sun, although they face competition down south. Indeed, the Williams brothers are due to visit English League One outfit Rotherham United.
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Neither was involved in Airdrie's crucial 2-1 win over Hamilton Academical in the Scottish Championship yesterday.
News of Celtic's interest in the midfielders comes as their pursuit of Lennon Miller looks to have taken a blow.
Belgian outfit Union Saint Gilloise are reportedly set to make a £5m move for the Motherwell youngster this summer. Brighton owner Tony Bloom is said to be 'driving' the move, with the view of a future switch to England's south coast for Miller.
Celtic manager Brendan Rodgers currently has a wealth of talent available to him in the engine room, although it remains to be seen what the summer transfer window may hold.