The Turkish giants have agreed a 10 million euro fee for the Netherlands playmaker and offered a contract, but Sneijder has stalled over a decision.
The 29-year-old has also been linked with a move to the Premier League, with Liverpool and Manchester United tipped as possible buyers.
But Galatasaray director Semih Haznedaroglu said they would not leave the offer open indefinitely.
He said: "We can't force him to come here if he doesn't want to. Perhaps he prefers to play in the Premier League.
"He has to give us an answer as soon as possible because we have done all we can. Perhaps he'll give us an answer today, but all this delay isn't ideal.
"All this waiting is no good for us and we'll look for an alternative. It was the same situation with Kaka. We did everything possible without any success.
"We can understand that there is no rush from Sneijder, but we have done our job. We've got an agreement with Inter and made the player an offer.
"We need a decision from him, a yes or no."
On Monday, Inter president Massimo Moratti expressed similar sentiments, saying: "It would be professional if he would make his decision by the end of the day."