I doubt that. Klopp might be a football romantic, but not even he would take over a club that promises him a net spend transfer budget of €10M per window. That is where they stand right now.
Liverpool is not stupid. They have been working to replace Coutinho since August, but so far nothing has worked out to their satisfaction. It´s not like Barcelona came with a surprise offer on Jan. 1st and Liverpool are now scrambling for a replacement on Jan. 7th.
The worst thing Liverpool could do is spend money for the sake of spending money to chase the top 4. Would you rather increase your chances to make the top 4 now by spending €110M on Lemar or wait till the summer and set yourself up properly for the next 4-5 years with a goalkeeper, central defender, defensive midfielder and winger? Even in this market, if you apply it smartly, you can do a lot of damage with that sort of money.
I´m Liverpool I seriously think about Aubameyang. That is somebody, who is actually worth €75M for his on-pitch production. Question is whether you want to deal with the off-pitch BS that comes with it. Mahrez for €55M would also be a great deal. Lemar €100M+ is a huge risk, but maybe they think his potential warrants it.