I have an optimistic theory...
Gylfi was willing to sign for us for around 35-45k a week, but then Spurs came along and offered 50k+ a week. Right. The media start saying that Spurs are the new favorites for him because they offered more money, but how do they actually know that Gylfi thinks Spurs are more attractive to him? Did he actually tell them so? The media are basically just saying that Spurs are the favorites because they offered him a better deal. Now, you might be thinking that why didn't he just reject Spurs outright if he wants to come here, but I think it's only reasonable for him to try and get a better deal with us because he has sort of 'proof' that he's more valuable than what LFC have agreed to pay him.
Anyway, I think he hasn't decided yet, which is why neither club has announced anything yet...