The 27-year-old spent a month at Oakwell earlier this season, scoring once in four appearances.
BBC: Garry O'Connor
Kay began his career as a centre-half at Barnsley, making over 200 appearances for the Oakwell club.
BBC: Huddersfield sign Tranmere's Kay
But the millionaires from Chelsea came to Oakwell and we did it again.
BBC: Buoyant Barnsley target Cup final
The win was Barnsley's first at Oakwell since March, but Robins said his side was better than that record suggested.
BBC: Robins delighted with Tykes win
He made six changes to his side for the trip to Oakwell - and had to make two first-half substitutions.
BBC: Barnsley 3-2 Burnley
Hughes will be disappointed City were not more prolific in front of goal, but the return leg at Oakwell on 31 July should be a formality.
BBC: EB Streymur 0-2 Man City
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