The four-day league match is to be held at the Rajkot Municipal cricket ground, said a media release from the association.
While Pujara played in the two-Test series against New Zealand, Unadkat toured with the India 'A' team to New Zealand in August.
Arpit Vasavada will lead Saurashtra in the four-day match.
England are set to play four Tests in India after arriving in Mumbai on October 29.
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