No side in Champions League history has recovered from four goals down. But Barca’s hopes were raised by the sensational form of Lionel Messi in Saturday's 5-0 rout of Celta Vigo.
"We will give everything from the first minute to the last," Rakitic told Spanish TV station Movistar. "We will try and hopefully we can produce a miracle."
Messi scored two spectacular individual goals to open and close the scoring. The 29-year-old Argentine had a hand in all three other goals too as he teed up Neymar for a sensational chip and crossed for Samuel Umtiti to score his first Barca goal, while Rakitic was also on the scoresheet.
In their first outing since coach Luis Enrique announced he will step down at the end of the season, Barca produced a compelling 90 minutes. It followed on from Wednesday night’s 6-1 demolition of Sporting Gijon.
"The match against Vigo was one of our best performances in the last few months, without doubt," Enrique said. "If I had to choose the way in which we would go into the Champions League game against PSG, it would be very similar to these last two games: scoring lots of goals, the team gaining confidence and the players getting stronger.
"I think we are in great form for a very difficult tie. It is a tie that is not lost yet.
I am sure we are going to have opportunities to get ourselves back in it and we will try until the death."
Enrique's name was chanted by an enthralled crowd at the Camp Nou on Saturday night. Banners were also raised towards the end of the match willing Barca's players to believe in the most unlikely of comebacks against PSG. "The fans value a lot what these players have won, the hunger they have and what they show in every game," added Enrique.
"In my time here I have never once seen a poor attitude in any of my players.
"Barca fans should be loyal and, above all, have confidence that the team can come back."
The Catalans top La Liga with 60 points after 26 games. Real Madrid, who won 4-1 at Eibar on Saturday night are second with 59 points but have played one game less.