Their budget would be gone on him. If he goes go there, he won’t solve all their problems and they’ll be scraping pennies together to try and plug other gaps.
They need about 3/4 new midfielders, not just 1.
If I was him, I’d be steering clear of the team in decline and going to a team whose coach progresses midfielders and are (currently) levels above the other Premier League team in for me.
Tbh, Liverpool need to try to repeat what they did a few years ago but with Brighton instead of Southampton. Caicedo & MacAllister would massively improve them. As you say, I can't imagine why they would put so much of their kitty into 1 player.