The Portuguese, who undertook the role in 2010 following the departure of Otto Rehhagel, has lost just four of his 41 matches in charge and led his side to next year's tournament in Brazil with a 4-2 aggregate play-off triumph over Romania.
Santos' contract is due to expire before the finals, but he is keen to continue his good work after Greece achieved back-to-back World Cup qualifications for the first time.
"We are in Brazil and we are pleased," he said after the second-leg draw in Bucharest. "I said that, at the right time, we would speak of renewal.
"Now I can say 'let's sit down', then we'll make the decision for the good of all.
"Come together for Brazil and then we'll see. My heart tells me to stay. Nowhere have I been so loved as in Greece."
Santos guided Greece to the quarter-finals in UEFA Euro 2012 and will be hoping to maintain their eight-match unbeaten run ahead of the finals.
