Pujara played for the club in the closing weeks of the Championships and scored 219 runs at an average of 54.75 in their last three games.
Derbyshire's elite performance director Graeme Welch said the county is in talks with Pujara regarding a potential return in 2015.
"We've spoken to Pujara already and he seemed quite keen to come back.  He integrated into the team brilliantly and I think he enjoyed the lads here," Welch said.
"He wants to test himself in English conditions, so this is probably the best place for him. The stumbling block could be that he has IPL commitments and a tour of Bangladesh, so we'll have to look at their schedule and try and get somebody in for those three months that he isn't here," he explained.

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