Fresh off spinning Australia into a web in the white-ball matches, AAP understands Theekshana and Wellalage have both entered Sri Lanka's camp.
Their arrivals come after Sri Lanka's reserve spinner Praveen Jayawickrama tested positive to COVID-19, ruling him out of the contest.
Teenager Wellalage was Sri Lanka's best bowler in the one-day series win over Australia last month, taking nine wickets at 22.33.
The left-arm orthodox bowler troubled Australia with his variations, just months after starring for Sri Lanka at the under-19 World Cup.
He had initially been left out of the main squad, only picked as a stand-by member and released out of the camp before the first Test.
However he has now returned to the group, and Jayawickrama's COVID case could open the door for his elevation to the full-time squad with no other frontline spinners selected.
A potential debut in the finale of the two-Test series on Friday could also loom.
If selected, Wellalage would be an option to replace struggling left-arm finger-spinner Lasith Embuldeniya, who was underwhelming in the first-Test loss.
Embuldeniya was Sri Lanka's best bowler last year, but has taken just 1-177 in his past two Tests.
A spinning wicket is again expected, however it will likely be slightly more friendly than what was served up for the series opener.
Uncapped mystery spinner Theekshana would also present a different challenge for the visitors if selected, spotted with Sri Lanka's squad on Monday after originally missing selection.
Sri Lanka coach Chris Silverwood admitted after the hosts' 10-wicket loss in the first Test that his four-pronged spin attack had underperformed.
Ramesh Mendis was by far Sri Lanka's best, while spinning allrounder Dhananjaya de Silva was grossly underused.
Jeffrey Vandersay also took 2-68 with his leg spin on debut while Embuldeniya went wicketless.
"Our spinners failed to put pressure on the opposition," Silverwood said.
"We failed to push them."
Meanwhile Jayawickrama's positive test came after Angelo Mathews also contracted the virus in the first Test.
Mathews is free to play in the second, while all other Sri Lanka players have since tested negative.
