Sangakkara, arguably the greatest Sri Lankan batsman, finished his 134-test career last week during the second test in Colombo which India won to tie the series at 1-1.
The 30-year-old Tharanga played the final test of the series against Pakistan but made way for Sangakkara for the first two matches against India.
"In his last match he hit a couple of 45s. He went out only because Sangakkara came in," Mathews told reporters ahead of the test starting on Friday.
Off-spinner Tharindu Kaushal, the most successful bowler for the hosts with 12 wickets, was doubtful for the third test with a thumb injury on his bowling hand, Mathews said.
But paceman Nuwan Pradeep, who missed the second test with a hamstring injury, was fit and available for selection.
With the retirement of Sangakkara, Mathews said Sri Lanka were still undecided on their batting order.
"We're trying to get our combination right to see who is best in what position," Mathews said. "We'll have to give it a bit more time for that, and then try and stick to a combination.
"In the past two series we've not made too many changes in our batting line up, but with Kumar Sangakkara retiring now, we've got an opportunity to test those players in different positions."
India are also poised to make changes to the line-up that won the second test convincingly in Colombo with opener Murali Vijay and wicketkeeper Wriddhiman Saha ruled out with injuries.
Team director Ravi Shastri said India were also not rigid on their batting order, having promoted Ajinkya Rahane to number three at the expense of the struggling Rohit Sharma in the second test.
"In this team, no one owns a batting position. It all depends on the situation," former India captain Shastri said.
"We will play horses for courses and see what the situation and the opposition demands.
"We play only for one reason and we play to win. Now we are in a position where if we can win this test, we win the series which is massive."
(Writing by Sudipto Ganguly in Mumbai; editing by Amlan Chakraborty)
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