Southee may replace Australian seamer Doug Bollinger, who is yet to recover from an ankle injury that led to him missing the World Cup.
Sources say that since Bollinger could be unavailable for the cash-rich event, the CSK management has decided to seek a replacement for the injured pacer from the IPL governing council.
The New Zealand pacer was in good form during the World Cup, emerging as the highest wicket-taker for his country with 18 scalps. His performance was one of the reasons for New Zealand reaching the last four in the competition.
Southee has played 13 Tests and 51 ODIs for New Zealand, taking 35 and 70 wickets respectively.
In the shortest version of the game, he has 22 victims from 19 T20 Internationals, with best figures of five for 18 against Pakistan in Auckland last year.