Real Madrid have made a £137 million ($188m) bid for Paris St Germain's France forward Kylian Mbappe, according to reports. Mbappe is out of contract at the Parc des Princes next summer and has so far refused to sign a new deal, despite PSG's attempts to get the France international to commit to the club. France's L'Equipe maintain PSG's position remained unchanged, with the Ligue 1 club determined to keep Mbappe until at least the end of his contract in June next year even if he could then leave for nothing. Spain's Marca said the move was a first step by Real, who have long had their sights on the 22-year-old World Cup-winner who scored 42 goals in all competitions for PSG last season and has reportedly told PSG that his dream is to move to Madrid. The As.com website quoted Real sources as saying, however, that the fact money was not an issue for PSG was an obstacle for Real. Any sale of Mbappe would allow PSG to recoup some of the costs of Lionel Messi's salary package after they signed the Argentina forward and six times Ballon d'Or winner from Barcelona earlier this month. PSG ended last season with only one major trophy, the French Cup, after losing the league title by one point to Lille and crashing out in the Champions League semi-finals. Real, now managed by Italian Carlo Ancelotti, were runners-up domestically last season to city rivals Atletico. Mbappe has scored 133 times and made 63 assists in 174 games for PSG in all competitions and has helped them towards 11 major domestic honours, including three Ligue 1 titles. He arrived from Monaco on an initial season-long loan in 2017 and was signed permanently for £165.7m a year later.