The International Cricket Council has banned Kaushal's way of bowling a "doosra" -- a ball delivered with an off spinner's action but which spins away from a right-handed batsman - because it exceeds the level of allowed elbow flexion.
However, the ICC cleared the 22-year-old Kaushal to bowl his stock ball, the off spin.
Mathews said that he and the team management hoped to rectify Kaushal's doosra action and have it cleared as well. The two-test series between the two sides starts on October 14.
"We have a lot of trust in him."
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Both teams are in transition after the retirement of many experienced players.
Jason Holder, 23, leads the West Indies in a test series for the first time and the team is without players like Chris Gayle and Shivnarine Chanderpaul.
Coach Phil Simmons is suspended pending an inquiry after his criticism of selection of the limited-overs side for the Sri Lanka tour. Selection committee member Eldine Baptiste has taken over coaching responsibilities in the interim.
"No doubt it is a bit of a setback for us, but at this present stage all we can focus on is cricket," he said. "I hope the situation with him is solved, and solved quickly because we'd love to have him back. He's been a wonderful inspiration to our team thus far."
Sri Lanka is without a permanent head coach after Marvan Atapattu resigned last month, following successive home test series defeats against Pakistan and India.
Organisers announced that the series will be played for the Sobers-Tissera trophy, named after West Indies great Garfield Sobers and Sri Lanka pre-test era captain, Michael Tissera.