The 34-year-old Mathews was not a part of the squad that toured England recently and last played the Test series against Bangladesh in April.
Mathews is considering the step after him and Test captain Dimuth Karunaratne found themselves excluded from the contracts that were offered to Sri Lankan players.
Shanaka, who was named Sri Lanka's T20 captain last week, was not allowed to board the flight with his teammates on Monday over his failure to arrange a new transit visa to the USA.
Sri Lanka had a substandard day with the bat as they were able to post just 135 on the scoreboard.
The two-Test series, beginning Thursday, is part of the ongoing ICC World Test Championship.
Mathews took four wickets and bowled his full quota of 10 overs for the first time since 2015. It is his second four-wicket haul in ODI cricket and helped Sri Lanka complete a 3-0 whitewash in the series.
Angelo Mathews scored his maiden Test double century to help Sri Lanaka take a handy lead against Zimbabwe on Day 4 of the first Test.
Former Sri Lankan skipper Angelo Mathews has been recalled for the three-game T20I series between India and Sri Lanka, starting January 5
Sri Lanka's senior cricketers, including Lasith Malinga, Angelo Mathews and Dimuth Karunaratne have reportedly refused to travel to Pakistan for a three-match T20I and ODI series.
Sri Lanka completed their first ODI series sweep in more than three years as they defeated Bangladesh by 122 runs in the final game of the series in Colombo.
Angelo Mathews said that he is disappointed with his performance and is looking to start bowling soon to contribute more to the team.
Avishka Fernando scored a good century while Angelo Mathews chipped in with important overs and picked up the wicket of Nicolas Pooran as Sri Lanka beat West Indies by 23 runs.
Sri Lanka's Angelo Mathews has a message for his teammates ahead of the all-important World Cup 2019.
Matthews was Sri Lanka's highest run-scorer in their two-Test series against New Zealand, during which he was dismissed once while scoring 258 runs.
New Zealand was frustrated that rain ruined their push for a 1-0 series lead Wednesday.
The twin centuries were a coming of age for one player, a redemption for the other.
On balance, New Zealand won the first session, Sri Lanka the second and the third was shared thanks to Dickwella's late flurry of boundaries.
The reason cited by the authorities is that Mathews was deemed 'unfit' to play the game at the highest level and hence dropped from the side.
Sri Lanka suffered a humiliating exit from the Asia Cup as they were ousted in the group stage itself, succumbing to embarrassing losses to Bangladesh and Afghanistan.
Asked about the weather, Rohit admitted that it's not really pleasant and also felt that the group that was in England needed the break to rejuvenate themselves.
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