Los Rojiblancos are currently 10th in La Liga, and out of the European qualifying places.
But he told reporters: "The fact is that while there is life there is hope. There are many games, many points before the end of the season."
The former Arsenal player added that improving the club’s away form is important, with Sevilla having won their last four home league games but losing their last four away matches.
"We all seek an explanation to the poor results on the road. We have played well at home. What we are looking for is points away to improve our position."
Reyes also said that he has a good relationship with coach Unai Emery who took the role in January.
"With Unai I feel good and at ease, he gives me confidence and minutes on the pitch and I cannot complain because we all have to play and I cannot be selfish. Some days are better and some worse.”