The host gets its campaign underway with a match against Gujarat and will expect to come up trumps in the tournament.
Ashwin, who has been out of the India ODI side since last year's ICC Champions Trophy, will aim to be among the wickets and impress the selectors again.
The lanky off-spinner, who was recently snapped up by Kings XI Punjab in the IPL auctions, did well in the first two Tests of the series against South Africa before missing the third.
Vijay, on the other hand, who hasn't featured in the limited-overs format for a while now, will look to use the tournament to run into form ahead of this year's IPL.
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He has been picked up by Chennai Super Kings (CSK) at the recent auctions.
The team led by all-rounder Vijay Shankar is a mix of youth and experience and the presence of Ashwin and Vijay adds strength to the line-up.
Shankar said the presence of the duo would be a motivating factor for the rest of the squad.
Tamil Nadu had a short camp leading into the tournament and captain Vijay Shankar said they had prepared well and that the aim was to perform well.
The team's coach Hrishikesh Kanitkar said the availability of Ashwin and Vijay would be a boost for the team.
He said he was not concerned about Ashwin not having played white ball cricket for over six months and said he expected to him do well.
The coach also confirmed that Murali Vijay will be opening for Tamil Nadu and the choice of the other opener will be made ahead of the game.
He also said the return of paceman Aswin Crist from injury was good news and added it remains to be seen how he goes in the tournament.
The Aditya Tare-led Mumbai, without Shreyas Iyer and Shardul Thakur, away on national duty, will expect the likes of Surya Kumar Yadav and Akash Parkar to step up.
Of the other teams in the fray, Maharashtra and Andhra Pradesh will be expected to spring a surprise or two.
The latter did well in the Ranji Trophy and failed to qualify for the Super League phase of Mushtaq Ali Trophy, losing out due to an inferior net run-rate.
Tamil Nadu starts favourite though surprises can't be ruled out in the limited-overs format and will aim to begin its campaign against Gujarat in a positive manner.