PSG v Chelsea: Paris St Germain aim for statement Champions League victory to convert their cash into credibility

Midfielder Blaise Matuidi believes the experience of playing together has made PSG a better team than last year (Getty Images)

For almost a year, they have been waiting in Paris for another night like this. Joining the elite of European football is difficult but winning a Champions League quarter-final against a current member is a good way to go about it. This time last year Paris Saint-Germain almost knocked out Barcelona. Against Chelsea they have an even better chance.

Ever since Qatar Sports Investments bought PSG in 2011 they have been pursuing one of the oldest challenges in sport: converting money into credibility. The main means of doing this is the Champions League. PSG are not going to do much for the global brand of Qatar simply by winning Ligue 1 for the next 10 years, as Uefa president Michel Platini has predicted they will.

PSG are not embarrassed about their ambitions. "In five years' time we want to be one of the best clubs in Europe," president Nasser al-Khelaifi said recently, "and to win the Champions League."

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Ezequiel Lavezzi, PSG's Argentine winger, claimed this week that "this is our time", although even victory in this tie would not necessarily make them favourites for the trophy. There are better teams and this is only PSG's second year among the elite.

Chelsea know better than anyone how elusive the Champions League trophy is. It was in the ninth year and under the eighth manager of Roman Abramovich's ownership that they finally won it, and even then under extremely unlikely circumstances. Manchester City, approaching the sixth anniversary of their takeover by the Abu Dhabi United Group, have not reached a quarter-final yet.

The PSG striker Zlatan Ibrahimovic, speaking in Paris, admired Chelsea for their progress. "Experience is an advantage, and Chelsea have more experience than PSG in the Champions League," he said. "We are in a situation today where Chelsea were eight or nine years ago, when the club owner took over and put in big investment, just as PSG are doing."

But what Ibrahimovic has seen so far – and what lured him from Milan to Paris in the first place – gives him confidence for the future.

"I've seen big changes in the two years, developments on and off the field that I haven't seen elsewhere," he said. "The people behind this project aren't aiming low or medium. These people aim more than high."

Tomorrow night is a chance for PSG to show that they belong on this stage and in this company. So far this season in the Champions League they have done well, winning their group before beating Bayer Leverkusen 6-1 on aggregate in the last 16. But, as L'Equipe argued this week, "what is still missing is a resounding win".

Last year, in PSG's first meaningful meeting with a European super-club, they nearly got it. Carlo Ancelotti's side managed to fight their way off the passing carousel at the Parc des Princes, earning a 2-2 draw against Barcelona. They took the lead at the Nou Camp and with 19 minutes left were going through to the semi-finals – until Lionel Messi limped on and Pedro scored.

The tie showed the world that this is a very serious unit. "Nothing has done more for the sporting image of PSG," said L'Equipe, "than going out with honours from the Champions League last year." The challenge now is to go one better and reach the semi-finals.

There is certainly confidence in the camp that they are better equipped this time. "There is a big difference," Ibrahimovic said. "We know each other much better today than we did last year. Last year, everything was new and we played as individuals. This year it is more of a collective, and our game is better."

Blaise Matuidi, the engine of Laurent Blanc's three-man midfield, picked up on the same theme. "We have more experience, we know more and we have learnt how to play together," he told Le Parisien this week. "We have grown up and turned a corner, and now we must show it."

Blanc's PSG have been showing it all season. They have been relentless, winning their last nine games in all competitions, and are 13 points clear of highly fancied Monaco – who hope to go through this process as well – with seven games left. They should retain their league title this month.

The easiness of the domestic league might be the one thing most likely to stop them in Europe. PSG simply do not have the experience of playing competitive opposition every week and, even with Monaco's own heavy investment, it is not inevitable that their wealth will trickle down.

PSG will have to raise their game against Chelsea and it will become clear over the two legs just how good they are. But Ibrahimovic is confident that this side have levels that they have not even shown yet. "The tougher the games you play," he said, "the better you become."