The Turkish club have been courting the playmaker in recent weeks and recent reports suggest that the transfer will finally be resolved one way or another.
Oguz Altay, the chairman of the Galatasaray supporters club, Tweeted that the Inter midfielder would have his move confirmed by the end of the week, writing: "I just finished a meeting with Galatasaray chairman Unal Aysal. He told me that there's almost an agreement with Sneijder. Thursday or Friday the deal will be done."
That is contrary to club official Semih Haznedaroglu's view, who admitted that Cimbom are still waiting for a reply from the former Real Madrid man after tabling a contract offer.
"We can't force him to come here if he doesn't want to. Perhaps he prefers to play in the Premier League," he told Bugun.
"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 [on Tuesday] but all this delay isn't ideal."
Haznedaroglu also warned Sneijder that the club would begin looking for an alternative if they continue to wait for confirmation or otherwise from the 28-year-old.
He continued: "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."