The Royals are looking for a replacement for Australian paceman Ashley Noffke, whose spell at New Road will end in mid August after being extended by a fortnight, and have held talks with Mishra.
Mishra has made five Test appearances for his country, the last of which was against England in December, and three one-day internationals.
He took seven wickets on his debut against Australia in Mohali two months earlier including five for 71 in the first innings.
The 26-year-old also turns out for Delhi Daredevils in the Indian Premier League.
Worcestershire chief executive Mark Newton admitted: "Amit Mishra is certainly on a list of players that we are talking to.
"But I must stress that he is one of many players that we are talking too.
"If you get can a work permit through in a month then you have done extremely well."
After Noffke's departure, bottom placed Worcestershire have a further five LV County Championship matches plus five Pro40 League games to play before the end of the season.
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