The 27-year-old goalkeeper has been regularly touted as a possible target for the Spanish giants and he came close to joining them in the summer of 2015, before the move fell through at the final hour.
Manchester United are known to be very keen to keep hold of the Spaniard and they are said to have offered him a new and improved contract to get him to commit his long-term future to the club.
Now, transfer insider McGarry has claimed that there is the offer of a new contract on the table for De Gea this summer, but his future will not be decided until after the World Cup.
Speaking on the Transfer Window podcast, McGarry said: “My information is there has been a contract offer on the table for a long time and it keeps improving.
“De Gea has gone to World Cup with the latest offer on the table and is waiting to see what happens in Russia and at Real Madrid this summer and then he will make a decision.”
Manchester United are on the lookout for a number of new signings this summer as they look to try and build a team capable of winning the Premier League next season.
The Red Devils finished in second place in the table last season and without a trophy under Jose Mourinho.
MORE: Man United latest news
MORE: Arsenal latest news
MORE: Chelsea latest news
MORE: Liverpool latest news