Madrid currently sit fourth in the Liga table - 19 points behind leaders Barcelona - and despite having won the Champions League in each of the last two seasons are widely being written off in their last-16 tie against the Ligue 1 outfit.
Pressure is building on manager Zinedine Zidane, with European silverware now their only chance of picking up a trophy to end the campaign after they were also knocked out of the Copa del Rey by lowly Leganes.
But Heynckes - who guided Madrid to the Champions League title in 1998 during his sole season in charge at Santiago Bernabeu - believes the Blancos have what it takes to beat Neymar and co.
"That Madrid is going through a low in the league at the moment is, in my opinion, quite normal, especially if you have won the Champions League twice and been Spanish champions too," he told Goal in an exclusive interview.
"In addition, Real have given away three very good players in the summer with Alvaro Morata, Pepe and James Rodriguez, perhaps to save salaries.
"They have not bought big and thought that with the young players they can compensate for that. You need a really good mix between young and old, between experienced and hungry players.
"Nevertheless, you must not write off Real in the Champions League. They have much more experience than Paris Saint-Germain. Much more! I believe they will win the tie.
"They have a good team for playing in European competition. When we first won the Champions League again in 1998, we finished fourth in the league. I know from personal experience Madrid should never be underestimated."
Heynckes himself guided Bayern through the Champions League group stages alongside PSG in Group B, setting up a tie with Besiktas in the last 16.
The Bundesliga champions have not won Europe's biggest prize since 2013 but are many people's dark horses for the competition this time around after Heynckes resurrected their poor early-season form under Carlo Ancelotti.
Heynckes, though, feels that the form and finances of Premier League clubs is making his own side's task of winning the tournament more difficult, and is unsure whether they will be able to keep competiting in years to come.
"We want to become Bundesliga champions, we are not yet. We also want to be successful in the German Cup and in the Champions League.
"In the Champions League, it will certainly be very difficult, because there are top teams, who - in part, with huge costs - have greatly improved their squads in the transfer market.
"It will be increasingly difficult for the Bundesliga and also for Bayern Munich to be as successful internationally as Bayern have been before in their history.
"There are always cycles in football. Recently, Real Madrid have been incredibly successful, before that it was Barcelona in a certain period of time. Bayern Munich were in 2013 and also in previous years. So there are always snapshots.
"Right now it is said that the English Premier League is the best and at the moment it might be like that. But the English teams have to prove that now in the knockout phase of the Champions League."