The Asian Football Confederation president also said any candidate who does not have "a minimum number" of votes should not stay in the contest for the February 26 vote, piling pressure on the other three campaign contenders.
South African media are already speculating that the only African candidate Tokyo Sexwale could withdraw this week, though he denied this to AFP.
Asked who how many candidates had a chance of winning the presidency of the scandal-tainted FIFA, the Bahrain sheikh said: "Realistically for the five, I think two."
Infantino is the UEFA general secretary, and will speak at a London conference tomorrow to outline what he will do in his first 90 days if elected president.
The other three candidates are Sexwale from South Africa, Jordan's Prince Ali bin Hussein, a former FIFA vice president, and Jerome Champagne from France, a former FIFA official.
Speaking in English and Arabic, Sheikh Salman said he was increasingly confident of victory.
"And now we are approaching the election date and after all the last contacts with the confederations and the national federations, I am confident and optimistic and I can see that things are improving day by day."
He added: "From my point of view things are more than good."
All 209 FIFA member associations will vote at a special congress in Zurich for a successor for Sepp Blatter, who stepped down and was subsequently banned from FIFA, following corruption allegations engulfing football's governing body.
"You have to leave the door always open, you cannot shut the door on any candidate."
He was speaking in Doha after attending the finals of the AFC Under 23 championship, which finished yesterday.
Infantino was also in Qatar over the weekend, as well as Sexwale.
Sheikh Salman added that anyone who had no chance of winning should now consider dropping out of the race.
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