The Sri Lankans were also hopeful of spinner Rangana Herath being available before the last eight clash.
Mathews suffered soreness in his Achilles tendon while batting during Sri Lanka's win over Scotland on Wednesday and did not take the field for the Scots' run chase.
A team spokesman told cricket.com.au he was "100 percent sure" that Mathews would be fit for their quarter-final on March 18. He said the skipper has not been sent for scans, but would take rest and be assessed again in the next couple of days.
The experienced Herath missed his side's pool A matches opposite Australia and Scotland due to a finger injury.
"I think he (Herath) has about an 80 percent chance of playing in the quarter-final," opener Lahiru Thirimanne said after the win over Scotland.
"I feel he will be fit," he was cited by cricket.com.au as saying on Thursday.
In the meantime, Sri Lanka have flown in off-spinner Tharindu Kaushal as cover for the left-armer.
The positive projection on Mathews and Herath would be welcome news for Sri Lanka during a Cup campaign that has been riddled with injuries.
Dinesh Chandimal tore a hamstring while batting during the islanders' 64-run defeat to Australia last Sunday and has been replaced in the squad by Kusal Perera.
Paceman Dhammika Prasad, slow-bowling all-rounder Jeevan Mendis and batsman Dimuth Karunaratne are already out of the tournament. Sri Lanka's quarter-final opponent is yet to be finalised, but it's likely to be South Africa.