Because, above all else, the Premier League club don't need to generate further income. They have 160 million euros to spend as it is - and, in any case, they know that they would be quoted fees higher than the market value of any possible replacements if they were to sell Coutinho. The standing of their American owners, Fenway Sports Group, took a major hit after parting with major stars such as Xabi Alonso, Fernando Torres, Javier Mascherano and Luis Suárez. FSG's chief shareholders, John Henry and Mike Gordon, are mindful of how those departures weakened the team, and how much it has cost to reconstruct it.
And sanctioning Coutinho's sale would in all likelihood work against Liverpool when stars such as Roberto Firmino and Sadio Mané receive offers to leave (and the club anticipate that happening next summer). The Reds want to avoid a situation of "You let him leave, now you have to let us leave too". What's more, this is not the time to be letting a key figure go: not in a season in which the aim is to mount a title challenge in such a competitive league - or at the very least retain a top-four spot - and have a good Champions League campaign.