Tendulkar is just 172 runs away from surpassing the 11,953 clocked up by retired West Indies captain Brian Lara -- a task within the reach of the Indian batsman who likes Sri Lankan pitches.
The star averages 111.66 from six Tests in Sri Lanka with four centuries. His last Test in the country was in 1999 when he cracked a half-century and a hundred in the Asian Test championships.
The 35-year-old already holds three major batting records -- the highest number of centuries in Tests (39), and the most runs (16,361) and hundreds (42) in one-day internationals.
Australia captain Ricky Ponting (10,099 runs) and India's Rahul Dravid (10,098) are the only active members of the elite 10,000 club.
Tendulkar, known for his flair and flamboyance at the crease, returns to Test cricket after four months due to a groin injury.
"He (Tendulkar) is too good," said Sri Lanka's senior wicketkeeper-batsman Kumar Sangakkara. "We know for sure that he is going to come hard at us at some point in the series and our bowlers will have to get him early.
"I know it's not going to be easy, but we have to hit the right areas to apply constant pressure on the Indians. And Sachin's wicket is a prized possession."
Tendulkar is one of the five veterans returning to Test cricket to boost India's chances of avenging their 2-1 defeat on the last tour of Sri Lanka in 2001. The others are Test captain Anil Kumble, Dravid, Sourav Ganguly and Venkatsai Laxman.
India will pin hopes on experienced players to win the first away Test series under Kumble, whose side has so far lost in Australia, but won at home against Pakistan and South Africa.
Off-spinner Harbhajan Singh returns to the side after a five-match ban for slapping team-mate Shanthakumaran Sreesanth during a domestic Twenty20 match in April.
The tourists' pace attack also looks sharp with the presence of Zaheer Khan, coming back after a spate of injuries, and the fast-improving 19-year-old Ishant Sharma.
Dinesh Karthick looks set to pip Parthiv Patel for the wicketkeeper's job left vacant by Mahendra Singh Dhoni, who has opted out of the Test tour due to fatigue.
Sri Lanka, always formidable at home, go into the series after beating South Africa, England and the West Indies in the past four years.
Sri Lanka captain Mahela Jayawardene said the series would be closely contested as both sides had "quality players".
"We enjoy playing India at home or away. It's always been a tough challenge. There is good rivalry with our neighbours," he said.
Off-spinner Muttiah Muralitharan, Test cricket's leading bowler with 735 wickets, is prepared to unsettle the Indians on his country's low, slow pitches.
The hosts have another surprise weapon in Ajantha Mendis, a spinner with clever variations who could make his Test debut after proving his credentials in one-day internationals.
India have already failed once against Mendis, who grabbed 6-13 to script Sri Lanka's victory in the Asia Cup final in Pakistan earlier this month.