Internazionale are doing their level best to rid themselves of the Dutchman and his £160,000-per-week wage, and Galatasaray were thought to be on the verge of a deal.
But now the Reds have supposedly come in with a very late bid and matched the £8.2 million from Gala, so what would Sneijder at Anfield mean for the team?
Sneijder is a pure No. 10. He sits in the hole behind the forwards and drifts between the defensive and midfield lines. He's a mercurial passer, but he's also surprisingly mobile.
Here's a diagram from Euro 2012, when the Netherlands took on Germany.
Joachim Loew's 4-2-3-1 met its identical counterpart in Bert van Marwijk's 4-2-3-1, leading to the classic midfield stalemate between two overloaded sides.
The difference-makers were Mesut Ozil and Sneijder, who tore around the pitch to try and initiate something for their respective sides. Sneijder, in particular, dropped deep, filtered out wide and provided thrust behind a toothless Robin van Persie.
Ozil was the more successful of the two, creating room for Mario Gomez to work his magic, but Sneijder's efforts in a limp, lifeless Dutch team were probably more impressive.
He fulfilled a versatile and demanding role under Jose Mourinho for Inter, and never for one second looked like he wanted to "float" like a Ganso would.
Undeniably, he'd fit.
He's a world-class player, if a little rusty at that. His "lockout" from the Inter team due to a contract dispute will harm his immediate production, but any club that lands him can consider themselves lucky.
The mobile nature of Sneijder would complement Steven Gerrard's new-found form behind the energetic Jordan Henderson, as explained by B/R's Karl Matchett:
Henderson might not be the greatest technician but his first touch is very good and he has brought bundles of energy to the team over the past month, as well as doing plenty of the backtracking and running beside Gerrard in midfield when Liverpool don't have the ball.
The 4-2-1-3 very quickly becomes a true three in midfield with someone with the work rate of Henderson in the team.
Gerrard, then, is deployed deeper. With the opposition intent on closing out the space in their own defensive third as Liverpool probe, probe, probe their way around the penalty box, the midfield sits in front of the defence to deny the Reds any chance of easily breaking through.
Substitute the energetic Henderson for the energetic Sneijder, and the Dutchman slots into the system without any major surgery needed. It's harsh on "Hendo" due to his rapid development and good form, but you can't pass up on a deal like this if it pops up.