The Red Devils have been linked with the Dutch international for some time, and were rumoured to have been close to securing his signature under former boss Sir Alex Ferguson.
However, a deal failed to materialise and Sneijder left Inter Milan to join the Turkish giants earlier this year.
But with David Moyes desperate to add some creativity to his engine room, the Premier League champions are ready to make a fresh offer for the playmaker.
The 29-year-old has long been hailed as one of European football’s top talents, and despite his form having dipped in recent years, United are still thought to be keen.
Gala are believed to be far from willing to let their man leave, but the Old Trafford side may look to sway their stance by offering either Nani or Antonio Valencia in exchange.
Sneijder himself may consider a big move, with Oranje boss Louis van Gaal having urged him to switch to a top league in order to boost his chances of making his nation’s squad for the 2014 World Cup.
Chelsea have also been linked with the midfield maestro.