Patil will be flying to Mumbai for the keenly awaited match after India entered the final by thrashing Pakistan at Mohali yesterday, Rashtrapati Bhawan sources said.
The President has been following the game and had watched the India-Pakistan semi-final match.
The Mohali encounter provided the "setting" for a "re-engagement" between India and Pakistan with Prime Minister Manmohan Singh and his Pakistani counterpart Yousuf Raza Gilani mixing cricket with diplomacy.
Reports from Colombo said that Rajapaksa will fly to Mumbai for the India-Sri Lanka final.
"The President wants us (Sri Lanka) to win the World Cup as a tribute to Muttiah Muralitharan who retires from international cricket after this World Cup," Rajapaksa's spokesman Bandula Jayasekera told reporters.
The Sri Lankan President and his three sons were keen spectators on Tuesday night when Sri Lanka beat New Zealand to reach the final to meet India.
Rajapaksa had visited the Caribbean when Sri Lanka reached the final of the 2007 World Cup with Australia.